I did some more research on this question. A contract that pays the player no matter what, whether they play or not, is called a guaranteed contract. Guaranteed contracts are rare in the NFL because injuries are so frequent. Only a small number of superstars get them.
The norm for NFL players are provisions that allow a team to cut a player at the beginning of the next year. So, the usual rule is that a player will always get paid for the current season, even if they do not play at all, but if they are unable to play due to an injury then the team can release them and terminate the contract the next year, as long as they decide to do so by a particular date, which is usually in March. Note that if a player cannot play due to injury, usually they get paid injury pay which is less than their full pay, but is still a substantial.
For star players, the amount of guaranteed pay is larger, often several years of the contract. So, for example, a $100 million contract might have $25 million guaranteed. Also, many star contracts have an "injury bonus" clause that pays additional money if the player suffers a career-ending injury. So, in that case, the player would receive the guaranteed money plus the injury bonus.
Longer-term contracts for super stars are not usually fully guaranteed. Usually, the team has several options to extend the contract. So, for example, a contract may have a 3-year guaranteed phase, plus a 3-year option which allows the team to automatically retain the quarterback for another 3-years at the same rate if they pay an additional sum of money as a bonus.
Contracts are also affected by the collective bargaining agreement between the owners and the player union. This prevents certain types of contracts from being binding for long-periods of time. When the collective bargaining agreement lapses, then it resets many of the conditions of individual contracts.
Drew Bledsoe's record $103 million dollar contract in 2001 featured an $8 million signing bonus and a $6 million injury guarantee. Only 3 years or so of Bledsoe's contract was guaranteed, so after he was traded to the Bills in 2002 (who assumed his contract), it was easy for the Bills to cut him in 2004, because relatively little guaranteed money remained on his contract. Bledsoe then signed a 3-year deal with the Cowboys, but it was an ordinary deal, only guaranteed for the current season, not a superstar deal. When his play became disappointing in the 2nd year, he was cut and he retired.