scope of 'everybody': infelicitous use of 'it'

Irene Heim claims the second 'it' is not felicitously used in this sequence of words. It must sound awkward.

1. Everybody found a cat and kept it. It ran away. (source: (5) on page 225 of 'File Change Semantics and the Familiarity Theory of Definiteness')

What would be an alternative then? My mind tells me 'the cat' and 'the cats' work here, depending, respectively, if they found one cat together, or if each of them found one cat, with possibility of some of them sharing one here and there.

Does connecting the two sentences solve the problem?

2. Everybody found a cat and kept it, and it ran away.
3. Everybody found a cat, kept it, and it ran away.

Also, I think splitting the first sentence makes the first 'it' infelicitous too. Am I right?

4. Everybody found a cat. They kept it. It ran away.

In my opinion Heim is wrong about this example. I don't know why the it is infelicitous in the Original example, but it doesn't seem to be for any of the reasons Heim gives. The reason for my saying this is that the it sounds ok in the following examples:

• Everybody found a cat and kept it. It always ran away the following day.
• Everybody found a cat and kept it. More often than not, it ran away the following day.
• Everybody found a cat and kept it. Invariably, it ran away.

The occurrences of 'it' in the Original Poster's examples (2) and (4) seem more or less felicitous to me too.