Searching for defensive & flexible playing style GM

I think of Kramnik. he's still way up the top ten-- though I have no idea if he teaches. but more importantly, why is it a requirement that your teacher "have" your playing style?
that's an odd thought, for me.
More important than their playing style is their Teaching Style... does it work for you? are you seeing the game in a different way?
---
if you are just looking for master games that are both defensive and flexible. Kramnik would be a fascinating study. Also the current world champion, Magnus Carlsen.

I've read a couple of times that Fischer did not have a style.
Also check out the Waitzkin videos on youtube. He constantly mentions that tries to go with the flow and take adventage of what his oppenent's moves leave behind.

Defensive & flexible style of play.
So searching for that style of GM and learn them.
Could you recommend GM player have this style of play?
Play the board, not the "style"

"Building a repertoire ... we will take the idealized situation of someone starting from square one ... The first step is to think about your personal style. Do you prefer open, tactical positions or closed, strategic positions? Does an attack on your king make you nervous, or are you happy so long as you have a counter-attack? Do you prefer main lines, or something slightly offbeat? Next, look at the various openings available, and see which ones fit in with your personal style. ..." - GM John Nunn (1998)
"... these days all grandmasters know very well that chess isn't only about playing good moves. In the majority of positions, there are a number of possible moves of roughly equal merit, ..." - GM John Nunn (2014)
"... we can see from the above that players who are happy as White to play for a small edge in a queenless middlegame have a number of lines where they can achieve the sort of position they want. Even in other variations, the willingness to settle for a near-equal endgame, rather than trying to obtain an objective opening advantage, makes one's whole job of opening repertoire management very much easier. ... With his superb intuition and depth of positional understanding, [Petrosian] was accustomed to treating the opening relatively flippantly, and did not normally strive very hard to gain a theoretical advantage. ... it seems to me that for many players below master level, having a repertoire where there is minimal need to prepare could in fact be quite attractive. It must be remembered that, despite its shortcomings, Petrosian's approach proved good enough to wrest the world title out of the hands of Botvinnik, one of the best-prepared players ever. ..." - FM Steve Giddins (2003)

Or just realize styles are MYTHS AND WEAKNESSES.
Ahhh ... the master of the smart-arse comment strikes again.
The truth is not so simple. Even if having a style is a sign of weakness players do have recognisable styles. Factors that affect your style are your chess vision, what do you see easily, what is more difficult, the positions that you have studied more deeply and are happier to play, the amount of risk you are prepared to take, whether you rely more on calculation or intuition and so on.
"You play what the position asks for, not what your style wants"
And this is a deliberate wind-up. What idiot would think "I have such and such a style so I will play this way?". That is not the way it works. Your style is part of you. You study the board and you chose a move that you believe to be strong. Your choices reveal your style.
"The style is the man himself " - Buffon
Or go back a bit further and study "Iron Tigran" Petrosian's games and writings ("Petrosian's Legacy").