We have a Home shared with several people. If we remove/stop sharing the Home with someone, do they receive a notification?
Don’t know, but it should be easy enough to test. Ask one of the others to remove you and see if you get notified. Ideally, you should trust this person to add you back after the test is complete 
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It probably does. Since they will be notified to pay for the services they consumed as part of being in the family earlier.
They will ask them to provide the billing info or else notify that their data will be lost for example for iCloud, they will lose Music subscription etc
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I got this from TakeControlBooks
Removing a Family Member
You can remove a family member age 13 or older at any
time:
- Go to Settings > iCloud > Family.
- Select the family member you wish to remove.
- Tap Remove.
- At the prompt, tap Remove again.
The removed person immediately looses access to shared
purchases (though they will remain on any devices until
deleted), the Family Photo Stream, Family calendar, and
everything else Family Sharing entails.
The removed family member receives a notification of the
removal
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They will most probably get a notification about that, as we get notifications about almost everything today.
But, If I want to remove somebody from something like that, I would normally have a good reason for that, and therefore I would not care, if the become aware of it earlier (via the Notification) or later (because the where not able to get access anymore.
They will learn about it anyway, and I wouldn’t care about that…
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Clarification: the person is not part of the Family Sharing. The Home was shared independently (like a guest).
From the feedback I will assume they will receive a notification.