It's all very country specific

If your visa expires while in Brazil, they'll still let you out with a relatively small fine (something like $8 a day), also won't affect your ability to return to Brazil in the future.

In places like Russia your sponsor has to extend your visa and pay significant fines and/or bribes before you'll be allowed to leave... and it can take weeks. In Japan, overstayers are automatically arrested at immigration, detained for 1-3 weeks and then deported with a ten year ban.