What are the impacts of closing STEM departments? To encourage new answers, I will award the bounty to any new answer. (e.g. answer and you will get the bounty) I understand this question is difficult to tackle and do appreciate all new insights.
According to this UK report:

There were 48 UK institutions offering physics degrees in 2005. This is 31 fewer than there were in 1994.
Since 1996 26 universities have ceased to offer chemistry degrees.
5 [mathematics departments] have closed since 1999.

While the report may be from 2007, this is still a current issue. The Royal Society for Chemistry has reported on a proposal to close the chemistry department at Bangor University. Apparently, Bangor Needs Chem.
Additionally, Bangor University no longer has a mathematics department (source). Also from Bangor University, the Computer Systems Engineering major states:

This degree has been designed especially for candidates without the usual qualifications in Mathematics and Physics to be able to pursue their interest in electronics and computer science to degree level.

Looking specifically at the words &quot;without the usual qualifications in Mathematics,&quot; doesn't this speak negatively to the reputation of the college and its graduates?  Is there a benefit (e.g. and in addition to financial) to closing STEM departments?
In summary, what are the effects (both positive and negative) of closing STEM departments? It is preferable if answers draw upon both theory (research studies, government reports, etc.) and practice (historical studies, your original research on past events and effects).
While the examples are from the UK, the question is about the effects of closing STEM departments in general and not specifically in the UK.
I can't give you a 100% answer (your question is kind of too wide) but I will try to give you some ideas:


The UK evaluates all departments of universities and research institutes on a
regular basis by a so-called Research Excellence Framework (REF). A bad REF evaluation might force a university to shut down a department. This is because universities are only allowed to teach a subject if they also do well received research in this field. Similar evaluation evaluations might be in place in other countries.
It might be a financial issue of why a department shuts down. Too few students and too high costs (in STEM there are often not enough good students applying)
"without the usual qualifications in Mathematics" I would not see this necessarily as a negative point. If you allow people with different backgrounds into a degree you might create a cohort of interdisciplinary graduates that might be in demand in industry. (They might not be competitive with e.g. pure math graduates but how many people really work in pure math later?) But it might also be due to the previous point that not enough people apply with a strong enough math background.
One more possible reason is that the university is not able to hire/hold sufficient professors in STEM fields as the pay in industry is usually much better and people with strong technical background might be aggressively recruited away. 


Impacts:


It is difficult so say what the impacts are as they are university specific but some degrees will not be offered anymore and/or they get external lecturers for e.g. math courses in non-STEM-degrees.
On a whole population level: Fewer people with STEM degrees means
fewer qualified workers
On the positive side: The university might have free-up resources in
order to persue other fields more intensively - but that is more a
strategic decision.