Going over this again, but Kumoko might be able to BFR. Kumoko has teleported many other beings, without effort, to pocket dimensions of her own making that require no energy to maintain (since she stores a ridiculous number of her clones in many different pocket dimensions at all times). Without Dimensional Manipulation, one would not be able to escape this. On top of this, Kumoko has the ability to interfere with the magic of others, as stated by Chapter 330 of the Web Novel, allowing her to effectively keep her opponents trapped in this dimension.
I'm going to withdraw my statement, Kumoko does have a win condition, and going over Ain's abilities up to now, only Ruler of the Abyss may be able to counter this, but I am unfamiliar as to exactly how this ability works. If it allows Ain to enter the abyss and then exit to the battlefield, Kumoko can just send him back into a pocket dimension (or anywhere else, for that matter). If Ain's control of the abyss allows him to escape and reenter the battlefield before the BFR time rule is up, I would actually say this match is inconclusive. If he cannot, this would be Kumoko's win.
E: oh and Mauer seems to be exactly one of the many things that Kumoko does with her own dimension portals. Ain, from this description, does not travel through them? Can he? Does he ever? Leere could kill Kumoko, but does this skill have a cast time? Is it avoidable? If so, Kumoko would transfer her soul to any of her clones.