The stun strategy in Doctor Who: Legacy involves stunning the enemy indefinitely. Originally stun characters were stronger, with shorter cooldowns and longer stun durations, which led to a very easy means of defeating even expert levels; that led to them being weakened to their current state.
Notably, no stun character has a cooldown of less than 9. Most have stun durations of 2 turns at maximum rank. Incidentally, many of their rank 6 powers are the same as their rank 5 powers. The upshot is that a full-stun team needs to be fully dedicated to stunning: all five companion choices need to be stun characters, since it's not possible to indefinitely stun an enemy with only 4 companion powers. (Use of the War Doctor might allow some leeway but as a Doctor power it's less reliable.) Simply put, upgrading any of the powers even one step in either factor (cooldown or duration) would have a dramatic impact, as it would allow a full-stun team that can also tech in another character (for stats or for a different power). It also means, currently, that you can only indefinitely stun one enemy at a time (only 3 companions stun all enemies, so for 4 out of 10 turns only one enemy could be stunned).
Another way the strategy was nerfed is enemies that make themselves immune as the first thing they do, disallowing you from stunning them (since the strategy can't be implemented for the first 9 turns to allow for cooldown). There's a hole in this, though, which is that immunity only lasts for a finite number of turns. If the player can survive that many turns they can eventually stun the enemy indefinitely. The difficulty of course is in surviving that many turns, but it's actually quite feasible with the amount of passive healing available via perks. With maximum passive healing, the player will heal after each turn from <10% to 43%+, from 10%-40% to 28%+, and from 40%+ to 48%+, which means the enemy can only win if their maximum damage output exceeds 28% of the team's maximum health (with 20k max health, the enemy needs to be able to deal more than 5600 damage in one turn, and do so on a very narrow band of health with the team starting the turn at just over 10% of max health). Of course, the hole in the strategy isn't necessarily viable, since it's time-consuming to perform (~100 turns tend to take over 5 minutes, even just swapping two gems with no match, so if the enemy makes itself immune for 999 turns then it takes an hour or more to outwait the immunity).
So I came up with this twist on the old strategy as a means to beat (2nd+) Expert 8th Doctor when more conventional strategy just led to him and a Toclafane reflecting all and bombing all my gems (which puts you in a bind of taking damage regardless of whether you match the bombed gems). The Master in that level makes himself immune for 999 turns (and also eliminates his weakness to yellow, but that's not relevant to this strategy). He also has various other powers, but the main point is he won't use the relevant ones (i.e. summoning Toclafane, reflecting attacks, bombing gems) until he's been damaged enough; if you do nothing, he'll just alternate between attacking (base 7k damage, which can be reduced by 20% to 5600 with perks), stunning a character, and using his frenzy power. Simply put, with maximum passive healing and damage reduction from perks, and 20k+ maximum team health, it's actually impossible for him to kill you until you've dealt enough damage to him. (20k max health is actually a slight issue, since most stun characters aren't very tanky, but with perks, OTB, and/or max level rank 6 stun characters it's doable.) So if you just stall for 1000 turns you can just stun him forever while whittling him down. Of course, like I said, it takes about an hour to stall for 1000 turns; then it could take another half hour or so to whittle him down. On the other hand, the strategy is pretty much foolproof, given the details of this particular level.
Of course, any number of things could be different in a level to make this kind of strategy not work. For instance, higher damage output from the enemy, more than one enemy, use of other confounding powers by the enemy.
In summary, thanks to the amount of passive healing from perks, indefinite passive stalling is possible (i.e. you can do it without making any gem matches), given the right conditions. With indefinite passive stalling, a full-stun strategy still works against an enemy that makes itself immune, although it may take a while.
Furthermore, this strategy shows the precarious balance of stun characters. Two more stun-all for 2 turns with cooldown 10 or less and a full-stun-all team would be possible (as opposed to full-stun-one). Lower cooldown or increase a duration even to 3 (without higher cooldown as with Ianto Jones +; however, a second companion with cooldown 10/duration 3 would also do it) and a full-stun team could be made with only 4 companions devoted to it. Even something as innocuous as adding more tank stun characters would increase the range of enemies you could stall indefinitely with passive healing while using a full-stun team.