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The prefix in- can mean "in" or "into" or similar, as in inire.
It can also mean "non-" or "un-", as in infelix.
Both meanings of the prefix are attested, but I am not familiar with any case where both readings of in- are possible.
Is there a word with which both meanings are attested (or otherwise reasonably defensible)?

This question arises from this earlier one and especially comments to the answer by Draconis.
I am looking for something like illapsus meaning both "in-fallen" and "non-fallen".
I imagine participles, especially those that have become adjectives in their own right are a potential source of such ambiguous prefixes.

I'm inclined to agree that participles are a likely source, as you suggest.

An example that springs to mind is innatus. As the perfect participle of innascor it means 'having been born in', etc. A little surprisingly, as that of innato it would mean something like 'having been floated upon' (perhaps, for instance, hydrargyrum innatum est ferro, though I can't find a proper attestation, and Latin might better express this the other way round).

On the other hand there is innatus, used adjectivally by Tertullian — Innatus deus; an non et innata et materia? (Lib. adv. Hermogenem) — which appears to mean 'not born'.

There is also the pair intego, intectum, 'cover over' and intectus, used adjectivally for 'not covered'.

I imagine that a search for further (and maybe more convincing) instances could be tedious, but these may suffice to indicate that the two-readings possibility exists.

It is worth pointing out that native speakers of Latin were well aware of the ambiguity referred to by Joonas in his question (directional/locative prefix IN- vs. negative prefix IN-). For example, consider the ambiguity of invocatus ('called upon' and 'not called upon') that is comically exploited by Plautus in the following text (Pl. Capt. 1, 69ff.):

Iuventus nomen indidit Scorto mihi,

eo quia invocatus soleo esse in convivio.

Scio absurde dictum hoc derisores dicere,

at ego aio recte. Nam scortum in convivio

sibi amator, talos quom iacit, scortum invocat.

Estne invocatum an non est? est planissume;

verum hercle vero nos parasiti planius,

quos numquam quisquam neque vocat neque invocat,

quasi mures semper edimus alienum cibum;

For relevant discussion of the ambiguity of invocatus involved in 'called upon' (directional IN- + vocatus) and 'not called upon' (negative IN- + vocatus), please read the following note 1 contained in this English translation (The Comedies of Plautus. Henry Thomas Riley. London: G. Bell and Sons, 1912).

NB I: Other similar examples of ambiguity like the ones commented on by Tom Cotton and cnread are: oratio inscripta est ((I) 'the speech is unwritten' and (II) 'the speech was inscribed/signed' (e.g., with the author's name)) & inauratus ((I) 'not ornamented with gold' or (II) p.p. participle of inaurare 'to cover with gold').

NB II: I think it is also interesting to point out that in Latin there are very few examples of co-appearance of the negative prefix IN- with the directional/locative IN-. For example, the three ones found in Baldi (1989: 6) are: ininventibilis, ininvestigabilis, and ininvicem. Cf. this link for a more complete list.

The example that comes most immediately to my mind is invisus.

As the perfect passive participle of the verb invideo, it means 'looked at askance' (i.e., looked upon, but in a bad way), and it's regularly used, by extension, as an adjective meaning 'hateful' or 'unpopular.' Use of this adjective/participle is very common.

As the negative of perfect passive participle visus, from the verb video, it means 'unseen.' This is somewhat rarer, but OLD cites examples from such sources as Cato, De agricultura 141.2, Cicero, De haruspicum responso 57, and Apuleius Metamorphoses 5.3.