Short answer: Instagram does not send someone an unfollow notification. They can still discover the change by checking their followers or comparing their follower lists over time.
What changes when you unfollow?
Unfollowing removes an account from your Following list. You stop following their posts, although Instagram may still recommend public content from that account. Your following count should decrease once Instagram updates it.
It does not automatically remove that person from your followers. If they follow you, they can continue following you until they choose to leave or you remove or block them. Unfollowing also does not erase earlier messages, likes, or comments. It changes the follow relationship going forward; it does not undo your past activity.
If the account is private, you may need to send a new follow request to see its private posts after you unfollow. You can still visit a public profile without following it.
Can the other person tell?
They will not receive an alert saying that you unfollowed them. But no notification does not mean impossible to notice.
They might look for your name in their followers list. They might remember that you used to follow them. Or they might have kept an earlier copy of their follower list and compared it with a newer one. That comparison can show that your account disappeared between the two records.
A single follower list only shows the current state. It cannot establish when someone left or reconstruct a list the account never saved.
What if you follow them again?
You can follow a public account again. A private account may require a new follow request, which its owner can approve or decline. Following again is a new action, so do not assume it will go unnoticed just because the earlier unfollow was silent.
Want a quieter change? Consider muting
If you simply want to see fewer posts from someone, muting may fit better. You can remain a follower while controlling what appears in your feed. If you no longer want a follow relationship, unfollowing is the direct choice.
If your goal is to stop them from following you, unfollowing will not do that. Review Instagram's follower-removal, privacy, and blocking controls instead.
What if you want to know who unfollowed you?
Instagram does not give you an unfollower notification or a built-in history of everyone who left. To identify changes, you need a follower list from an earlier date and another from a later date. A missing account is a change to investigate; the lists alone cannot prove whether the person unfollowed, blocked you, deactivated, or became unavailable.
Our guide to seeing who unfollowed you on Instagram explains that distinction with an example. UnfollowPeek can keep and compare the Instagram exports you choose to import on your iPhone, without asking for your Instagram password.