I'm writing a thesis which consists in a literature review and I came across some articles whose titles seem to be appropriate for my research, but they don't have any abstract and their full text is unavailable. Before even trying to get those full texts, which might require some time and effort, my question is: are they reliable? I mean, what are the possibilities of finding a peer reviewed article which doesn't have an abstract?
It is impossible to say without actually examining them, but you can get a fair idea by knowing the journal in which they appear. If it is reputable, then the chances are that the paper is.
Also, there is a difference between not having an abstract and not having a published abstract.
You probably need to get the articles to be sure, however, but that is true of everything. See an academic librarian to ease your task. They can probably also give you advice on the reputation and reliability of publishers.
As to the literal question on papers without abstract, I would say that not having an abstract is becoming less common, but it not really a sign of quality. Shorter papers really don't need an abstract (or a discussion section) if they have a good introduction. This is the "say something once, why say it again" philosophy.
Many journals will not allow a paper without an abstract. The journal that published a paper of mine with no abstract now says "the article should include an abstract of at most 150 words" so it seems you might be able to publish a paper there without an abstract if you insist.
Of course, you still need to look to the paper to see if it has an abstract. No database covers all papers and has zero omissions.
It is quite possible that the answer is whatever database you are using does not have the abstract, rather than the original paper not having one.
This is quite common for older papers - many of the literature databases are stitched together out of all sorts of older databases, some of which had citation details only, and going back to add them in is a laborious task which may not be very highly prioritised.
Take Nature, for example. Web of Science has it covered since 1900, but abstracts are only included from ~1990. In Scopus, it is covered right back to 1869, but the abstracts only go to ~1950 (and seem to miss 1965-66 for some even odder reason).
And of course papers that are harder to find online may be more likely to be older, obscure, etc and less likely to be comprehensively indexed on databases. So it's unlikely to automatically indicate it's of low value or not worth investigating.