I was talking with a faculty member and her strategy is to submit to as many grant proposals even if the quality is not high. And in fact, one of her grants was accepted. Are there any benefits for a researcher or university in terms of number of grants submitted even if the quality is low-medium and they were not awarded?
There are a few reasons I have encountered for approaching things this way:
It's All Random
There is a perception among some people that, as long as you're writing a "good-ish" proposal (i.e. one that's not appallingly poor in its ideas or written style) that whether or not your grant is actually funded is something of a random process. Relatively low inter-reviewer agreement (see here: http://www.pnas.org/content/early/2018/02/27/1714379115) and scores that jump up and down between revisions helps cement this perception.
If one believes this - and one believes that their normal grant falls in this "good-ish" category, then it's logical to view funding as a function of how many grants you submit.
Similarly, if one believes this, the marginal benefit of polishing a grant vs. writing another is pretty heavily skewed toward writing another once you get it past that "good-ish" threshold.
I Need to Report Something
With tenure evaluations at many institutions still relying on funding and (arguably) not having caught up with the idea that junior faculty may be good researchers and not have secured a major grant by the time they come up for tenure, one may feel pressure to at least look like you're trying.
Note that this has plusses and minuses to it. I have seen people criticized for not going after the "good" money (NIH/NSF), but I've also seen people criticized for having an extremely low hit rate ("He submitted twelve grants last year and none of them got funded).
Grant Review as a Sounding Board
Occasionally, it's not clear what's fundable in a particular field - especially if some of the "Big Names" have certain territories staked out already. In those cases, someone pay use the shotgun approach to see if anything seems to catch reviewer's attention. In essence, you're hoping here not to get funded (though that would be nice) but to see if some of the applications get a decent score on the various scientific merit metrics, and if those have a coherent pattern to them.
As other folks have mentioned, there's definitely downsides to this, including that the applications aren't blinded, that the researcher or institute might develop a reputation, etc.
There are no direct benefits if the applications are not accepted. There might be some indirect benefits, if during the writing process the researcher gains feedback on their ideas and plans from colleagues or reviewers. Or, it might be useful to show evidence to your boss that, in the absence of grant income, you are indeed attempting to secure some.
But one important benefit is mentioned in your question already:
in fact, one of her grants was accepted
You've got to be in it to win it. There is definitely some unpredictability in the grant application process, in terms of who reviews it, who is on the panel, what mood the panel are in on that particular day, etc. So, (all else being equal) the more you submit, the more chance you have.
Importantly, there are also potential disadvantages of submitting large numbers of low quality grants. For example, NERC UK has instigated a "demand management" system for its standard grants, such that if an institution's success rate drops below 20% they will be limited in the number of applications they can submit the next year. The NSF (which is tagged in OP's question) places limits on the number of applications from an institution for a number of its grant schemes. For an individual researcher, this means that they probably need to get through an internal review before they can submit a grant application. In both internal and external reviews, it may not go down well with your colleagues/peers if you regularly submit low-standard grant applications, resulting in reputational damage.
The agencies I have applied to ask for reviews, and the applicant gets these reviews. Those can help to improve the grant proposal, to be submitted to another agency.
I would be hesitant to recommend such a "shotgun approach", as the reviews in the agencies I have applied for are not blind. They cannot be, because the reviewers are also asked to rate the applicant. With a shotgun approach I would very quickly get a bad reputation.
Some universities are not receiving many grants because they are not applying for very many. In one case I saw "submit more grant applications" as a strategic goal. In this case submitting many mediocre applications may help a faculty member get promoted.
Some universities reward faculty whose external grant applications are unsuccessful with internal research funding. There is some quality standard.
The more "random" the decision process is, the more benefit does this approach have. So, if rolling dice is a good approximation of how that particular funding body selects applications (or a program committee selects papers, by the way), this is a valid strategy.
Now, let's hope for the best that there are not very many funding bodies and IPCs like this.
When going up for tenure, junior professors often must show evidence of attempts to secure funding. Particularly at R1 schools where having external funding is an important part of the tenure decision, having this documented evidence could mitigate a lack of successful awards. Also, as others noted, a shotgun approach does sometimes work, and the exercise in grant writing helps flesh out one's research program and may suggest alternative paths of inquiry.