Solo mining Where do the coins go

[freedomno1]

My question is,
If you solo mine and are not part of a pool and it says GOT LP or Got Bitcoin really rarely etc
Where does it send the coins to and how do you claim them, a pool account updates your balance but how does it work for a solo miner, for example in GUI miner is it setting a path to your wallet etc and that's where it deposits and if no path is set what happens to those coins, I know that bitcoins are awarded in blocks and it takes months to find one so the question is more about Litecoins
Anyways sorry if that question seemed a bit messy but thanks for reading it
PS: Also what happens to mined coins if a pool is down