BELONGING TO AN INSTITUTION
This is a bit tricky in terms of it's relation to Greendale Community College since it's not exactly portrayed as a powerful institution but it is very noteworthy due to its significant impact in people's life that has been changed since they came here
By Choice
The classic example of this would be Troy, Britta, Shirley Abed, Pierce and to some extent Jeff, Troy simply choose to Greendale for his convenience as his place is within proximity to the college, Pierce on the other hand is looking out to keep an active mind and become very up to date with his presence, although the specific reason why he chose Greendale is unknown, it is plausible that he may also choose it for its convenience too. Jeff to a lesser extent could be considered a choice, as he intially stated in the pilot, he wants to have an easy path, he chose Greendale for it's low reputation and possibly quality
but otherwise he was in some sense forced otherwise. Britta simply chose Greendale solely on gaining educational awareness, no apparent other initial reason as to why she chose Greendale specifically, similarly with Abed and Shirley, although Shirley's purpose was to gain understanding of business path to allow her to pursue her own entrepreunial goals. Otherwise apart from these factors, by choice, all these characters in Community belong to a community college for one purpose as "Duncan" quoted "Second chance" to allow an individual and later a collective group personal growth across all aspects as explored throughout the series
For Power
There isn't a specific reason as to the character's belonging to Greendale would increase their power status due to it's floored reputation (at least in the beginning of the series). However, a different approach of power does come from one's "Awareness" and "Knowledge". Ultimately, attending Community College increases qualification of someone, as well as that, it increases one's awareness and knowledge on what they are mastering which is equal to power
as they are able to be more in control of their life as reflected also by both personal and group development overtime. The Idea of power is also narrowed down to Dean's involvement in the school, he actively improve the school using his weird incentives
as he is the power of the institution (rather a weak one we must say) despite joining the institution for reason to improve the lives of other, it is ultimately landed him in power and this is very evident in episode 3.08 (Documentry:Redux) although for Chang in season 3, his rise of Power within Greendale very significant in changing the course and development for the group and the school, acting out as a revenge for the study group and his sufferings, but also for his essential reason we will explore further
By Need
The necessity of joining Greendale Community College is reflected in Jeff's necessity to regained his qualifications for his career to resume, for Pierce it is for him to keep active and up to date as I mentioned last time, Shirley, Annie, Abed, Britta and Troy ultimately need them for the qualifications to pursue their own path in life
Chang on the other hand joined Greendale because he initially need an employment before overturned by the debunk of his qualifications in season 1, hence Chang then need Greendale for pursuing education and sense of "belonging" explicitly towards the study group, whilst third season, it has become apparent that Chang's necessity for survival has driven him to power towards the end of season 3, his job and place of living in the school has officially been incorporated basically entirely of his life at that point in time
By Force
Annie was one of the unique case that is quite forced to join Greendale, she cannot obtain scholarship due to her nervous breakdown in high school due to her drug influence, she is forced to choose Greendale as a path for her to gain higher education, In some sense Initially Troy was seen as forced to go to Greendale College as he lost a football scolarship, however it is revealed that he was afraid of his uncertainties about football, instead he chose a different path. Chang, by some circumstance, was forced to choose Greendale to work at initially due to the loose system of employment based on a comical judgement grounds of "Racism" acusations
Protection
I am personally struggling to find the idea of protection in belonging to Greendale Community College, based on past experiences, the school has been through many invasions and actual civil wars, although if the idea of protection is streched into means of "facilitating" then it has a well done job in accomodating it's students as a place for the group to grow, nurtured by the beloved Dean and have manage to continually survive against all odds
Pride
The pride within Greendale is similarly not seen very much in the actual reason people (study group) initially joined the school, however it was testified during the paintball invasion of episode 2.24 (For a Few Paintballs More) in the star wars themed episode in defending Greendale against the City College near complete overtake of the school. The sense of belonging to an institution that arised as a result of marginalised state of the group
Image
Episode 3.08 is a fine example of improving Greendale image in their idea of the school, also neatly wrapped around Dean's psychological breakdowns. Initial reason the study group joining Greendale wasn't based on their Image as well, however the group's existence and Dean's favouritism proved that the group is essemtial in improving the school's reputation and image, as their actions through saving the school and academic achievements has create a crucial change in the perception of the school
all these neatly wrapped under the theme of "second chance"