I couldn't find any law in Finland that mandates the liability insurance to Finnish rental cars (correct me if I'm wrong). There is mandatory traffic insurance for rental cars, but I couldn't find confirmation that it would have to cover liability too. Some webpages of Finnish rental companies stated that liability is part of the insurance and some didn't have an explicit statement of that at all. Probably the safest way is to ask prior or while making the rental deal if their insurance has such coverage. There is always some own risk part in case of an accident, but it can usually be reduced or eliminated with extra cost.
The following is additional information, as I misunderstood first that the question was about medical care insurance for the passengers:
In Finland people traveling to other countries take a travel insurance. It might be for one trip only or for any travel with specific terms. Most people (who travel at all) take the one that includes all traveling. So based on that I would assume that people traveling to Finland would be assumed to be insured by a foreign company.
Although the Finnish law requires to give medical care in emergency situations to anyone. If that person is afterwards identified as a non-EU citizen then the actual costs of the treatment can be billed later. For Finnish people emergency care would be almost free just a fraction of the costs are typically paid by the receiver of care.
I didn't find any Finnish companies selling insurance for traveling in Finland only and I don't know what their stand would be if you would ask them. But by a little googling there are European insurance companies that offer insurance for traveling in the EU (e.g. in here). And Canadian companies offering travel insurance in general (e.g. in here).
In my opinion this is not about cars or rental cars at all as the question is about the health and wellbeing of the people traveling.