League of legend rank question

If you lose enough games, yes.

League of Legends uses something called the MMR system, which is a score based off your wins and losses. If you win a lot of games in a row, your losses won't cost you as much LP. However, if you consistently loses matches, your MMR score suffers and eventually you will start dropping tiers. Take it from someone that learned this the hard way. XD

Well, first you would drop to Bronze 1, but only if you lose a lot of games in Silver 5 at 0 LP. You won't drop if you don't play, though.