How did this character survive?

Question

Near the beginning of Miss Peregrine’s Home for Peculiar Children,

Jacob’s grandfather, Abe, is killed by a hollowgast that had been working with Barron.

At the end of the movie, we see this character alive again, apparently because

Barron was killed by one of his hollowgast allies.

It would seem that this is because the events that caused him to be killed never happened.

How does this work, though? The timeline seems to go as follows:

1. Barron and the hollowgast killed him in the movie’s present.

2. Barron goes to Wales and

   kidnaps Miss Peregrine from the time loop.

3. Barron takes her to the present.

4. The children find

   a loop that connects to the present and mount a rescue there.

5. The hollow kills Barron in the present.

All of this seems to have happened after Barron killed the character in question, though (in his own personal timeline).

How did Barron’s death change any of this?

Answer 1

It's all timey-wimey, but my understanding of the events was that he did not save him, he was just able to visit him.

The London loop was six months in the past, and Jake stayed behind when the other children went back to the present. So he was able to go visit Abe and then make his way through the other loops to get back to the ship in the present time. They made it look like he saved him, but that would then negate his need to go to the island in the first place. I see it as just a way of allowing Jake to say good-bye.

Answer 2

I had a lot of trouble following the timeline stuff, but I got the impression that the last 30 minutes or so of the movie, which you say are in the present, are actually in January 2016, while the movie starts in the present (i.e., autumn 2016).  So Barron is killed in January 2016, before he goes to Florida for his encounter with Abe.

Answer 3

The ending does not make sense. At least to me. Here is what Emma tells Jake while they're aboard the ship on the way to Blackpool (the location of Miss Avocet's January 2016 loop):

Jake, you know what this means don't you? ... We have to get to our own time but you don't. You can continue to live in 2016... If we kill Barron, he'll be gone but time will carry on. He won't go to Florida, Abe won't die, and you can go home."

At least to me, it doesn't make logical sense that killing Barron would save the life of Jake's grandfather Abe. Abe died in July 2016, so theoretically killing a version of Barron from before then would prevent Abe's death. But that's not what happens; in Blackpool Barron speaks about Abe's death:

I tracked Abe Portman for months. All I needed was a few minutes to get the location of Miss Peregrine's loop from him. But no, Mathus couldn't wait. And instead, I had to masquerade as a psychiatrist for three weeks in Florida.

So Barron has already participated in the Florida events. So it does not make logical sense that killing Barron will mean that "he won't go to Florida [and] Abe won't die".

The movie logic seems to be something like "If you die in a loop then both your past and your future are completely erased from the timeline." I think that's the meaning of the statement "he'll be gone but time will carry on". But it seems impossible to come up with a model of time travel where that would make sense.