Is it possible to get a research assistantship between undergraduate and masters degree, while not enrolled as a student? I finished my undergrad in Electrical Engineering at the end of 2014, and since 2013 then I've been working on a startup that is soon going to fail.

I would like to apply for a Masters in 2017, and to strengthen my research profile in my resume, as well as earn letters of recommendation (which I sorely lack), I'm considering working under a professor/ at a lab for a year or so (in a research area similar to that I worked on at my startup). 

However all research assistant/research associate positions seem to be advertised only towards students currently already studying in a graduate (masters/PhD) program.

Is it common/normal/acceptable for people to work in a university lab between their undergraduate and masters, like I wish to? If so, what are these positions usually called in the US/Europe, if not Research Assistantship? 

To clarify, in addition to gaining experience, my main motivation would be to have a well known professor/someone at a well known lab recommend me, since I have a only one professor from my undergrad who would be willing to give me a strong letter of recommendation. I cannot expect anything from my present colleagues. Most applications seem to require 3 such letters.
Sure, it is normal to work for a university lab with only a bachelors or masters. However, none of the people I knew did this as a transition between undergrad and grad, rather they did it to transition out of research.

The job titles range widely though, especially across fields. I have seen job titles of "Research Programmer", "Research Engineer", "Software Engineer", "Systems Researcher", etc. This is in Computer Science so other fields may have something along the lines of "Lab Technician" or other domain specific titles.

If you want to do research, then apply to graduate programs that are relevant to you and attempt to contact potential advisors.