In law, yes - after 3 months, you should either be able to support yourself or get out. If you remember the recent deportations from France of the Roma - it was under this law.
However - if you've got the EU residence certificate, then that's a whole new question - I'm pretty certain they can't then deport you under this law (as you'll have a valid zameldowanie). Interesting legal minefield, though.
can non-polish EU citizens claim unemployment assistance here?
Yes - provided they have the EU residence certificate and they also comply with the relevant laws on being eligible for unemployment cash.
I'm sure it burns Polish-Americans inside that we superior Brits can claim cash from Poland and they can't.