Suppose a team won the Champions league this season (say Chelsea) but in their current league season they finished outside of the fourth place (say Chelsea finished fifth in premier league). Are the champions given the champions advantage to again participate in champions league out of the rules? And can you name some example of this situation happening to any team?
This has happened before. Liverpool won the champions league in 2004-05 season, but finished 5th in the EPL. They were given an exemption by UEFA and added to the first round of the qualifying rounds.
They managed to go through all qualification rounds and made it to the tournament that year.
UEFA later decided to allow the champions direct berth to the following year's tournament. Until 205-16 no association could send more than 4 teams to the Champions League. This resulted in the Tottenham Hotspurs missing out of the tournament despite finishing 4th in EPL in 2011-12 due to Chelsea winning the Champions league that year and ranking 6th in the EPL.
As of 2015-16 associations are allowed a hypothetical 5th team so the winner of the Europa League or Champions League can make the tournament without booting out a 4th place team in domestic leagues.