tl;dr– The saying itself isn't fallacious; this is, it can be apt to observe that a person who was characteristically more prone to a behavior than others would likely tend to be more prone to that behavior than others in the future.
Of course, misapplications of concepts can be fallacious. For example, someone who stole an item once wouldn't necessarily always attempt to steal things in any given scenario – that'd be an over-generalization
As a saying, it's a bit terse so that it can be referenced concisely.
A more verbose, detailed version of this saying might be something like:
If someone was once a "thief" – this is, if it would've been accurate to have described their character as being prone to thievery – then that someone, so long as they remain essentially the same person in the sense of having the same general personality, would tend to retain that characteristic of being prone to thievery.
Of course, the expression could be pretty silly if someone mistook it for being literal. For example, if a thief were imprisoned where there was nothing for them to steal, then, obviously, they wouldn't steal.
But, again, it's just a terse reference to the general concept of how people tend to retain personality traits over time, including propensities toward behaviors such as thievery.
Also worth noting that someone having a propensity toward a behavior, e.g. thievery, wouldn't necessarily express that behavior in every scenario. This is, even someone who would be predisposed toward thievery wouldn't necessarily be fully defined by that one characteristic.
Discussion: Crimes can prove someone doesn't have a red-line prohibition against a behavior.
Some folks can have red-lines for behaviors that they won't engage in or even consider engaging in. For example, many folks would never rape someone under any circumstance – that's a red-line that they won't cross, or even consider crossing.
When someone does something, e.g. steals, they prove that they were capable of doing that thing, and therefore prove that they didn't have a red-line prohibition against it.
Of course, someone who might rape/steal/whatever wouldn't necessarily engage in the same behavior every time – in fact, they might never do it again!
That said.. sometimes it's not an issue of knowing that someone will do the behavior again, but rather an issue of not being able to trust that they wouldn't.