Can government garnish a tenant security deposit?

If some agency is going after the tenant, then yes.

If they are going after the landlord, then they shouldn't be able to, but, they may not know that it's the tenant's money. Most states require that the landlord put the deposit in an account that makes it clear that this is the tenant's money. However, failure to do so is probably the most common mistake in landlord/tenant law. It could be that the tenant could contact the agency, and convince them that they have seized an account that they should not have.