Nobody has any right to claim dole in Finland if they haven't contributed to the system first. Say you're under 25, they force you to get an education before you get on the basic "labour market subsidy", which isn't dole as in "unemployment benefits" even.
That means-tested thing effects quite much, they've saturated it through the system. Also effects students, well, everybody.
The Finnish system has nothing to do with the UK system. EU means you have the same "rights" as any local, or as it is with KELA, the "unpayment office" you have no rights

The EU rule is that if you have been Xnum days on the dole in the UK, you can transfer your dole with you for Xnum days to find a job in Finland. If you don't find a job by then, it doesn't say you can claim similar or any dole in Finland after that. You need to go back in the UK etc. This for a general worker. Being a spouse then again is a bit different rules. However it clearly states for a person entering the Finnish labour market for the first time if they have not worked in Finland for 10 months they are put on the labour market subsidy after a 5 month "quarantine" period.