If he did kill frisk, he would naturally absorbs their soul (as he does with any enemy in dark souls) and nullify frisk dying, which does mean the chosen undead has a wincon. (assuming this cancels out their loads and resets)
frisk however, in theory can reason with the chosen undead, but in all realistic outcomes is he going to listen? chances are he runs at them and throws em in a shed or soul absorbs them.
In theory, if Chosen Undead grapples them and throws them in a shed, Frisk would be driven to reset. Maybe. Frisk really doesn't have an in character. Technically. 8-B Frisk is still a Frisk that is controlled by The Player first-and-foremost, all of their ACT actions are things Frisk would do, yes, but all of their actions are still decided upon and acted on by the player.
Plus, with the way that Frisk's Reset is worded in their wiki page, Frisk can choose to reset at any time... since the player can close the game and load back to their reset without Frisk dying, but that's probably too meta to be accepted.
Honestly, I don't buy Chosen Undead's Soul Absorption due to the above reasoning.
Their speed is equalized, so Frisk should be able to react to Chosen Undead's moves, and... Frisk has dodging feats, so if CD runs at them, they would do their best to dodge and attempt to reason with CD... Or just start Singing to activate their sleep manipulation hax since Frisk is an RPG character, so it is quite possible that they do the best move first. IDK. RPG Characters are weird in Verse Threads.
Additionally, CD doesn't have any resistance to social influencing and a lot of Frisk foes were folks that wanted to kill them in one way or another but Frisk managed to talk them down. Probably doesn't work that way, but it is a step in the right direction.
... Or nothing could happen, and CD and Frisk are stuck in a loop of incapping and resetting.