That depends on which country they have fled to and how much it was.
A Chinese individual who got a domestic loan and fled to the US is likely to not suffer any persecution in the US. Same as for a US citizen who fled to China.
If a British individual with a green card fled to the US and it was a loan of <1 million, it is unlikely that the US will send the US Marshals to find and jail the British citizen.
If a British individual with a green card fled to the US and it was a loan of several millions, it is now likely that the US will send the US Marshals to find and jail the British citizen and extradite him/her.
You asked about what happends to the individual, and in most cases, nothing actually happens. However, banks will seize assets in country of origin, will communicate with other national banks so that they will never lend money to that individual again or even refuse to open account, domestically or abroad. So for example, that British example, and borrowed money from HSBC ; it will likely be unable to borrow money or even open an account in Barclays in the US.
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