I can't speak for Finnish Schengen visa but I did the same when I was working in Germany. I was granted a working visa which was Type 'D' where I was allowed to travel within Schengen countries. I finished my employment earlier than I thought so I went back to the UK. I decided to go back to Berlin again for leisure with the same visa. I was allowed in without any problem. The immigration officer didn't ask me a question. I did that twice and I didn't have any problems.
My friend was in the same situation and the immigration officer asked her what she was doing there and she just simply answered that she's there for business and she didn't have any problem.
This doesn't mean that it would be the same for everyone. The best thing would be to check with the embassy of your point of entry.