score:2
I imagine it might be possible if not flying with luggage:
This assumes you have a direct flight Czech -> Singapore and not e.g. Czech -> Finland -> Singapore. No intra-Schengen legs. If you do, you can try to re-book your flight, e.g. go from Bulgaria to Helsinki directly and there board a Singapore flight without connecting leg.
This also assumes you're missing your Czech event because you're not exiting airport.
This also assumes that Czech airport (Prague?) has cleared non-Schengen transfer area and that there are flights from Bulgaria coming in before Singapore flight is departing, and you're on it.
Upvote:2
Your friend made a grave mistake somewhere
Connecting at Helsinki, if the trip from Singapore to Bulgaria was on one ticket, he should not have cleared Finnish immigration at all; thus, his Schengen visa should not have been "activated"
If it was on separate tickets (meaning luggage had to be collected) then he should in fact have specifically requested a double-entry visa, presenting the itinerary as evidence and noting that it's on separate tickets (meaning luggage has to be collected past immigration).
Unfortunately your friend is completely out of luck regarding the Czech event. Most, if not all, Schengen embassies will not process visas for people not citizens or legal residents of the country of location.