* to relieve - verb (infinitive form)
John relieves his coworker
You relieved him (past tense)
* a relief - noun
I provide relief for my cat
That was a relief (probably a better way to say the situation was a relief)
Now, normally, if we use -ING , its when we are making the verb present participle (to use in the present progressive tense) example:
* I am relievING you from your job
* She is relieving him from his shift
To your question: there are many verbs that use the -ING suffix that make it look like an adjective: calming music, relaxing music, soothing music, my running playlist, etc
Lets use some examples with relieving:
a relieving situation (this isnt commonly used)
a relieving letter (I googled and found this)