They generally don’t get to take it with them unless they are carrying it at the time, and other people will definitely step in to take their stuff eventually. Maybe the government, maybe the family, maybe opportunists. But this doesn’t usually happen right away.

Some stuff is explicitly seized at the time of arrest, there is a complex and opaque system of laws built around this. Some of it is seized as evidence. Some of that may be returned eventually, but usually not for a very long time, and much of it won’t be. Other procedures are used to seize things that seem valuable, originally intended to seize things that were actually criminal in nature or the product of crime. All of the details vary in different jurisdictions. Look up “Civil asset forfeiture” for more information. But not everything is seized. Lots of stuff is simply not interesting or valuable or there’s no legal justification to take it, so it’s just left behind. Often, the stuff just sits there, unused, empty, untouched. Technically it is still “theirs” even though “they” are gone. After all, they could yet be found innocent.

But possession, as always, is 9/10ths of the law. If the person’s family is still living there and takes it, nobody’s policing that or even disputing it. If someone else takes it, there’s probably nobody to complain.

Meanwhile, any fees or debts that are due are still due, even if nobody’s around to pay them. Nobody’s going to give the guy a break from his financial obligations just because he got arrested or deported. Your accounts were frozen? Oh that’s too bad, you’re still obligated to find a way to pay. Then we start seeing the people this money is “owed” to start to repossess things. It often only takes a missed payment or two and bam, it’s gone. Mortgage? House belongs to the bank now. Unpaid taxes or registration fees? Government will helpfully sell it for you to pay any fees, all sorted out now you’re welcome.

Like @Diplomjodler3@lemmy.world says, the cruelty is the point. Your losses of possessions are an unofficial part of your punishment, and the great part is many of them still happen whether you’re found innocent or guilty. It’s a convenient way of punishing people who are completely innocent along with those who aren’t quite guilty enough to be found guilty.