Suppose I've few coins for proof of stake, and suddenly my internet connection goes off or power down of my pc, what may happen if a transaction was in the middle, would I lose my coins which were in the middle of the transaction process ?
It's unclear what the question is.
If by "transaction" you mean solving a PoS block, then you cannot relay this new block to the network if you're offline, so the network participants will continue trying to solve that block. If you do not reconnect quick enough, another block will be found, and yours will soon be orphaned, so you lose the block reward you would otherwise have had.
If by "transaction" you mean you were sending a payment to the network, then no coins are lost, since the network does not know about this transaction, so non coins are moved, but they stay wherever they are.
Proof of stake doesn't require you to be online. You only have to have them on your wallet and they will grow just by that.