Was curious, so I checked. Leicester City did have a core of their champions win promotion (1st in the Championship) and then added very smartly. Of their 14 players with the most appearances in 2015-16:
1. Seven were in the side that won the Championship in 13-14: Schmeichel, Morgan, Schlupp, King, Drinkwater, Mahrez, and Vardy. That's the captain (Morgan), goalkeeper (Schmeichel), PFA Player of the Season (Mahrez), and Barclay's Player of the Season and Golden Boot runner-up (Vardy) from the title winners. A solid core.
2. Albrighton, Simpson, and Ulloa arrived before the 14-15 season; two of the title-winning 1st XI and Ulloa, who mainly was used as a sub in '16 but was their leading scorer in '15 as they escaped relegation (I was surprised Vardy only had five that year before exploding for 24.)
3. Fuchs, Huth, Okazaki, and Kante arrived before the title season. All four were 1st XI in '16, and Kante... what a player he was that season.
Also, Leicester staged a miraculous escape in '14-15: dead last after matchweek 29 with just 19 points, then went 7-1-1 to claim 22 of their final 27 points to finish 14th. The manager who led said escape got canned for his work, in came Claudio Ranieri who hadn't managed since getting fired by Greece in 2014, and we all know the rest.