I'm not too sure whether these has been brought up, but I'll just share. All these happened in real world and I think it should implement in future FMs.
More controversial off field matters on players which could affect their careers and bans: scandals, jail term, police cases, tax invasions and tragic deaths.
Retired players became club owners/shareholders like the 4 ex-man u legends with salford city.
More players expressed desires to leave club after a manager's interests and player's agent tries to talk to chairman/board and make it public.
Player interviews/reactions by medias after matches, or winning the MOTM.
Players or club captain become more involved of teammate's unhappiness due to manager's mistakes, formations and recent negative pre/post match talks.
Former/Ex-players have grudges against managers after unsuccesful spell on clubs. Players will not want to play for your club ever again.
Players clash with each other during a match. Remember Lee Bowyer and Kieron Dyer? Club to take actions against these players after that.
Players falling out with each other (in club or international level) due to personal and off field incident (Wayne Bridge and John Terry incident). Player(s) might decide to leave club in order not to face each other again.
Players involved in charity and other good campaigns.
Players feel insecure after new players of his same position are bought.
Players willing to take the pay cut to join the manager he wished to play for or his boyhood club.
Retire player numbers after player passed on.
Managers in constant talk with club captain about any good players recommendations, current player's roles suitability and other ideas.
Managers and coaches in constant talks/views about formations, systems and errors during matches and match trainings which the managers could do some minor tweaks/adjustments in trainings or right after matchdays to achieve better systems and formations.
Managers are given few more answers during pre/post match talks and Board interviews than the default 5 answers.
Managers having grudges against each other or from rival clubs for longer periods of time.
"tapping up" players through agents to be implement, just an idea. I know, it's not good..
Chairman/ board expressed interest through medias on managers from other clubs after their current manager's poor performance halfway through the season. After chairman/ board get their man, they will send a notice to managers to resign immediately.
Monthly Board meetings with managers about clubs issues, next transfer targets and budgets. After that, Board will inform you of their decisions (which Board may support you in every way they can to help you acheive your goals if you are performing well).
Board may try to strike a deal for players eventually after weeks of negotiating instead of "Player target ends in failure..."
Headline news of Fans' interview by media outside stadium about match predictions.
Street attacks, riots and fans' behaviour led to club being fined and possibly of fans facing stadium ban.
Street celebrations after winning any cup finals.
One minute of silence before match as a mark of respect due to some tragedies, death of ex-players/managers or hillsborough/munich air disaster remembrance (if playing on 2D/3D matches).
Clubs are able to sign young kids, as young as 10 year old for academies and mould into young stars and possibly play for future 1st team.
A few more in depth trainings could be implement, i guess.. Or maybe SI might got a new sets of training in store.
More hidden gems/unknown wonderkids around the world.
More playable leagues than in the current FM16.
More built in tactics in tactics column, like "Park the Bus" tactic and other new tactics that SI/FM may have thought before.
More goal celebrations in 3D match (you know, there are Nani's, Benjani's, Klose's, Bebeto's, Klinsmann's and many more).