More than 100,000 Russians have crossed into Kazakhstan since Russian President Vladimir Putin put the country into a state of partial mobilisation.
In a speech last week, Kazakh President Kassym-Jomart Tokayev described the fleeing men's situation as "hopeless".
For now, Mr Tokayev has vowed to "take care of them and secure their safety".
Kazakhstan has traditionally been a Kremlin ally but analysts say its open support for people Moscow may consider criminals is a further sign it could be drifting out of Russia's orbit.
Unlike other allies China and Belarus, not a single Kazakh official has voiced support for Mr Putin's war — and Mr Tokayev is taking an increasingly strident tone against it.
He's vowed not to recognise Russia's claims over eastern Ukraine or Crimea and he's promised not to help Russia bypass sanctions.
This is despite Mr Tokayev and his government effectively being propped up by a Russian-led military mission in January amid widespread unrest.
So could Ukraine's lightning offensive around Kharkiv not only have punctured Russia's depleted army but also its status as a regional power in Central Asia?
And could a diminished Russia be an opening for China to build even stronger ties with its neighbours?
'We can imagine ourselves in the same situation'
Since the dissolution of the USSR in 1991, Russia has sought to maintain influence among the bloc's 15 now-independent states.
Mr Putin himself declared more than 20 years ago that the former Soviet republics were within Russia's "sphere of influence".
Kazakhstan is the biggest former Soviet republic in Central Asia, both economically and geographically, and a significant portion of its population is ethnically Russian, particularly in the north.
While the two have long maintained good relations, Kazakhstan and Russia's relationship today is complex.
On the one hand, the countries have strong diplomatic, security and economic ties, according to Nargis Kassenova, a senior fellow in Eurasian studies at Harvard University.
"We're probably the most Russified former Soviet republic," she said.
"The Russian language is very widely used … we read Russian books, we watch Russian TV, we are inside the Russian information space.
"On the other hand, Russia violates the territorial integrity and sovereignty of one of the former Soviet republics, and we can imagine ourselves to be in the same situation."
In March, one Moscow official called for the "denazification" of Kazakhstan, the same justification Russia's government is using for its gambit in Ukraine.
In early September, in a now deleted social media post, deputy chairman of Russia's security council Dmitry Medvedev said Kazakhstan was an "artificial state" and Russia could turn its attention to the fate of its northern regions next.
Mr Medvedev later said his account had been hacked.
Temur Umarov, a Eurasion analyst for the Carnegie Endowment for International Peace based in Tashkent, said Central Asian countries faced "a very risky situation".
"Because they logically put themselves in the shoes of Ukraine and understand that when Moscow uses this narrative of artificial state [in Ukraine] … that the same logic could be used towards them."
No Central Asian country has voiced open support for Russia's war in Ukraine.
Still, any decoupling would not come without risks.
"So we haven't seen any country in Central Asia that supported Russia … but at the same time, we haven't seen any country criticising Russia openly," Mr Umarov said.
'Good ties with neighbours guarantee safety'
Mr Tokayev used a proverb in his speech last week — "good ties with neighbours guarantee safety" — suggesting he would not push so hard as to provoke a Russian response.
Andrew D'Anieri, the assistant director at the Atlantic Council's Eurasia Centre, says there was a balancing act for Kazakhstan and other Central Asian countries.
"Russia is a privileged economic partner in the region … especially in Kazakhstan. It accounts for roughly 40 per cent of commodities trade," Mr D'Anieri said.
"We talked to Kazakh officials here in [Washington DC], and they say that 'we are going to continue to trade with Russia, we have one of the longest borders in the world with Russia … we are going to rely on them for some things."
Still, it is evident that Kazakhstan's positions have not been welcomed in Moscow.
Russia has intermittently shut down pipelines Kazakhstan uses to export oil that traverses Russian territory in recent months — and there has been heightened rhetoric among Russian bloggers and hardliners.
"The rhetoric in unofficial Moscow is increasing, and I think that tells us something about how angry official Moscow is at Kazakhstan," Mr D'Anieri said.
'The shift from Russia to China is only going to continue'
As leaders gathered earlier this month in Uzbekistan for the Shanghai Cooperation Organisation meeting, Vladimir Putin cut a more lonely figure than usual.
He is known to keep leaders of other countries waiting.
Former German chancellor Angela Merkel was reportedly once left waiting four hours for a meeting with the Russian president in 2014.
But at the SCO meeting in Tashkent, Vladimir Putin was left awkwardly waiting before some leaders came to meet him.
"Putin being made to wait by the president of Kyrgyzstan is not something we see every day," Mr D'Anieri said.
Analysts say the war in Ukraine is accelerating cooperation with new partners for countries in Central Asia.
China has already formed strong economic ties in the region through its Belt and Road Initiative and Mr D'Anieri said it could look to form more.
It's notable that Chinese President Xi Jinping's first overseas trip since the start of the pandemic was to Kazakhstan earlier this month.
While Russian officials have made veiled threats against Kazakhstan, Mr Xi reassured Mr Tokayev, saying he "firmly supports Kazakhstan in safeguarding national independence, sovereignty and territorial integrity".
"China has been eating Russia's lunch in the far east economically for many years," Mr D'Anieri said.
"That shift from Russia to China is only going to continue."
'Three decades of independence did not pass in vain'
So could Russia's wager on empire lead to a terminal decline in regional influence?
"I would say that even before the war, it was inevitable that Russia's influence and Russia's soft power in Central Asia was declining," Mr Umarov said.
The post-Soviet generation — those born after 1991 — are now the majority in Central Asia.
Mr Umarov said many no longer looked to Moscow as an attractive cultural or economic centre of gravity.
Ms Kassenova agreed, saying "three decades of independence did not pass in vain".
"There is a generational change, and indeed, there is a demographic change … there is the foundations for trying to be more than just a satellite or client of Russia," she says.
As for Russia's future in Central Asia, Mr D'Anieri predicted its power would wane "in the short, medium, and long-term".
"Russia today is much weaker militarily and economically, and it's more isolated diplomatically … the invasion of Ukraine has really made Russia the big loser in the region," he said.
