loosened, loose end

Loosened or loosened ( one word ) is the past tense ( yesterday, or some time ago ) of "loosen", meaning to free from something that binds or constricts; to make less tight or to slacken--
I loosened the dog's collar; I don't know why he's still scratching at it.
He loosened the nut, but it's still won't come off.

Loose end or loose end ( two words ) means a free or unattached part; a part left unsecured--
Hold the loose end of this ribbon while I tie the bow, will you?
Here, use this to tape the loose end of those lights to the window.

Now that you know that, you can say--
"She pulled on the loose end of the string, and loosened the knot. We'll have to wrap it again."

Note--"at loose ends" is a somewhat old-fashioned expression meaning in an unsettled situation or undetermined position--
He has been at loose ends ever since he lost his job.
Note # 2--"loosen one's grip" means to slacken one's hold on something, intentionally--
Loosen your grip; don't hold it so tightly.
Not to be confused with "losing one's grip" ( participle of "lose" ), meaning to fail to grasp something, unintentionally--
He's losing his grip! He'll fall!
To "lose one's grip" may mean to lose one's control or mastery of a situation--
He can't handle the job; he's losing his grip.