Is there a way for a species to essentially become a living incubator of sorts? Not the other way around, as in Plausible ways for the alien species to be able to impregnate every and any species?, but only impregnated. The offspring produced by the host doesn't need to be related to the host at all, only the donor, but is this too complex for a species? And if not, how could it go about?
If "impregnated" means "getting genetic material in you from something else and using it to make your offspring" then yes. Bacteria do this. It is called transformation.
What is Bacterial Transformation?
Bacterial transformation is a process of horizontal gene transfer by which some bacteria take up foreign genetic material (naked DNA) from the environment... The process of gene transfer by transformation does not require a living donor cell but only requires the presence of persistent DNA in the environment. The prerequisite for bacteria to undergo transformation is its ability to take up free, extracellular genetic material... Once the transforming factor (DNA) enters the cytoplasm, it may be degraded by nucleases if it is different from the bacterial DNA. If the exogenous genetic material is similar to bacterial DNA, it may integrate into the chromosome. Sometimes the exogenous genetic material may co-exist as a plasmid with chromosomal DNA.
It is risky, taking up loose DNA from the environment and bringing it home. It might be a virus or a transposon. You have to keep your guard up. On the other hand if it is a remnant of something which is doing very well in your environment, and you are not doing very well, maybe that DNA has the secrets to success that you can pass on to your own offspring.
There are some examples of genes which have hopped not only across phyla but across kingdoms. Leghemoglobin is made by legume plants. Hemoglobin is otherwise strictly an animal protein but somehow these plants got hold of the code and now use it for their own purposes. Pretty cool!
Though the terminology is not the same, this happens all the time with parasites and/or 'friendly' bacteria. Virtually all animals have some kind of bacterial population living within them who use the host as a source of heat and nutrition and as a place to reproduce.
It doesn't take an enormous leap to scale this up to incubate a larger species (and probably already happens in nature somewhere). The question you then have to resolve is why the host-species would accept this: Is there some sort of symbiotic benefit? Are they bred specifically for this purpose? Are they unable to object?
There is a way that this could occur biologically, but it's a stretch and a half.
First, the womb would have to be a major part of your alien's biology, because it would have to be able to accommodate all kinds of animals (I am assuming that this is just limited to animals because it would be kind of difficult for a human to give birth to a fungus or plant, etc. Also, I'll be limiting what I cover to Earth biology, because I really don't want to deal with all of the problems of xenozoology.)
Then, there is the problem of actually creating the animal in the womb, because a large part of a fetus's biology is actually designated by conditions in the womb. Different chemical conditions across the womb decide what cells get produced. Additionally, there are some difficulties with actually getting nutrients to the animal and attaching it to the womb- if it even grows in the womb at all. After all, it is mostly only mammals that actually grow their young inside them, and most other animals lay eggs. Therefore, the alien would need an egg-laying apparatus. The decision of how to actually produce the child brings us to the third problem.
This third problem is that the alien would need DNA interpretation skills on a heretofore unseen level. Standard egg-sperm production could be done, but it would require a lot more resources than standard same-species reproduction and would be very complex. So, let's dive in.
The alien encounters an animal that it wishes to incubate. It acquires a sample of reproductive cells from this through (insert horrific biological explanation of a thoroughly sickening process), and once that is done, it proceeds on. Dependent on the animal, chromosomally based sexual selection is done differently, but usually the case is that two different sex chromosomes means one gender, and a pair means the other. The sex cells can only be obtained from the one that has a pair, and only that gender can be produced. That's just how it works. Anyway, once it has two sex cells from the correct gender, it can remove the DNA and this is where it gets really tricky. The alien's cells have to analyze the DNA and determine a key factor- how are the animal's sexual organs made. Once it has that, it has to reorganize its own organs to match that map, all the while keeping enough copies of the animal's own DNA to stop it from degrading. I'm no expert in this field, but I estimate that this process could take about 5 years. That was the hard part. From then on, it is surprisingly simple. The alien merely needs to produce a feasible egg such as the original host made, implant the DNA into that egg, hope and pray, and basically just go through a normal pregnancy (or egglaying and incubation, whatever is the case.) Then, with some luck (a lot of luck, this process would probably have an extremely low success rate), all that is left to do is let the young animal mature and in the case of sentience have a crippling identity crisis.