The word "thief" can be found and is fixed in English dictionaries, but "stealer" is not.
Katamba and Stonham write:
[.....] Usually perfect synonyms are avoided. Thus, it may be because thief already exists that suffixing the otherwise very productive agentive suffix -er to the verb steal in order to form *stealer is blocked.[F.Katamba, J.Stonham, Morphology, 2006:75]
At first blush, it can be inferred that stealer is both a non-existing and impossible word. However, searching Corpus of Contemporary American English, I found a number of sentences where the word "stealer" not "thief" was used. It comes to prove that "stealer" is, nonetheless, a possible word.
Why does it not make its way into English dictionaries then? Why not fill the shoes of thief?
After reading your post I looked at several online dictionaries and every one had "stealer" and defined it. Most included "thief" as a synonym. So I don't agree with your first sentence that "stealer" is not fixed in English dictionaries. I agree with Katamba and Stonham that "stealer" is used less but I think that examples of this are readily found. There are many words with synonyms that are used less frequently. Maybe "stealer" is used less because it is less pejorative at times when a thief should be spoken of very negatively.
I tend to agree with both Glenn and Dick. "Thief" gets 400 million hits on Google, "stealer" a mere 8 million. And "stealer" just sounds awkward (though admittedly less disparaging) compared to "thief." It kinda reminds me of when G.W Bush declared himself "the decider." Perfectly legitimate word, but just sounds unpolished.
Also, "stealer" is a homophone of "steeler," and so when spoken could lead to confusion about meaning.
I agree with Dick that stealer is less pejorative. And I agree with Heimhenge that the word stealer sounds awkward in isolation.
But it doesn't sound awkward to me when modified as in the following examples. To me stealer focuses a little more attention to the act of stealing, as opposed to thief, which focuses more attention on the condition or state of the person
Don't be a french-fry stealer!
Don't be a french-fry thief!
We have a pencil stealer in our office.
We have a pencil thief in our office.
Is anyone else thinking of Dora, the Explorer? "Swiper, no swiping! Swiper, no swiping! Swiper, no swiping!"