As it is very competitive to have tenure, I wonder if there is any case that someone holds a non-tenure position (e.g. associate professor) until the end of his/her career, i.e. until the retirement. If there is, is it a normal practice?
In the US system, it is generally not possible for a person to hold a tenure track but non-tenured position, such as being a tenure-track assistant professor, for longer than a few years (I think the typical tenure clock is 6 years plus extensions for life events like new babies). After that, the person will either get tenure or else they will have to leave or switch to a different class of position, such as "research scientist."
Research scientists or non-tenure-track professors, however, can easily have a full and comfortable career with nothing even vaguely like tenure involved, all the way up until they retire, go emeritus, or succumb to old age. This can happen both in traditional academia (see, for example, Dave Clark, or non-tenure professors at medical schools) or in alternate academic settings such as national labs and research companies.
Yes, it is certainly possible.
It not not necessarily the most "iconic" track, as most people assume a "Tenure Track" -> "Tenure" progression, but it's certainly far from abnormal. Here are a couple ways this could happen:
- Medical schools. I've applied for a number of jobs in medical schools, and seen others, where the position is not tenure-track for PhDs. Basically, this is because while they could make MDs make up their salary with clinic duty, the PhDs are utterly dependent on grant money, and in nearly/entirely soft money positions, the department wants to be able to fire them if they stop being able to support themselves.
- State institutions. There are some institutions where tenure implies an obligation by the state, and when the state isn't going to support a position, the institution may list it as non-tenured position that may still be permanent.
- Soft-money research institutes. Where I work now, which is somewhere you could absolutely have an entire career, doesn't have the ability to give tenure, and as such, unless you've got a joint appointment with a tenure granting department, tenure simply isn't a thing.
- It's entirely possible to have built a career out of adjunct positions, lectureships, etc., none of which had the prospect of being tenured.
Another way this can happen is via "professor of practice" positions. Some departments/schools, usually explicitly professional in orientation (e.g. business, information studies, some health fields, social work, sometimes even law), recruit full-time instructors from the ranks of practitioners as well as from Ph.D-holders. These positions are never (that I've ever seen) tenure-track/tenured, but they certainly can be long-term, covering the rest of the instructor's career.
(At most US institutions, since most professional schools issue graduate-level degrees as well as teaching undergraduates, the requirement is that an instructor without a Ph.D hold the "terminal degree" for the field, so, an ML(I)S for an information school, or a JD for a lawyer.)