In the case of Morant, who has a $34,005,250 cap hit for the 2023-24 season, the Grizzlies are potentially eligible for a DPE of $12,505,000, the amount of the non-taxpayer mid-level exception for 2023-24. Furthermore, if granted the DPE, the Grizzlies can do so through both signing new contracts or trading for incumbent ones, as long as a player is signed only for the remainder of the season, or a trade acquisition is in the final year of a pre-existing contract.
It was not always the case that DPEs had to be this way; in 2011, when Yao Ming was ruled out for the season, the Houston Rockets were given a DPE equivalent to the full MLE and used it to sign Trevor Ariza to a five-year deal, a term much longer than Yao was absent for. Since that time, though, the DPE has been clarified to now only be eligible for players in the final season of their contract (a caveat which further disqualifies any deals including future option seasons), when it comes to its use in trades or waiver claims (which are treated as a form of trade).
Mid-season free-agent signings for above the minimum salary are very rare, for obvious reasons. A waiver claim, of course, is even less likely. Ariza excepted, then, it can be seen how the DPE is mostly a vehicle used in trade, particularly when the injured party only got injured after play began.
However, any player acquired in this way – and it can only be one player, as it is not permitted to split the amount of a Disabled Player Exception on multiple players in the way that, say, a Mid-Level Exception can be – is not free. Any player acquired with a DPE is still paid their salary by the team, still counts against the salary cap, and still counts towards luxury tax calculations. And nor is the salary cap number of the injured player reduced in any way.