A subscription does not truly expire until the grace period has ended. I don't know what you mean by obsolete. Do you mean the plan was deleted somehow?

And, second question, is it also the reason why email on expiration are not send ?

Expiration emails won't send unless the plan goes directly into expiration state. So most likely, yes.

obsolete means that subscription end date is over (without grace period)

The subscription should be expired then. If the plan had a grace period, the user subscribed, then you removed the grace period your change is not retroactive. Existing subscriptions are untouched by future plan changes.

So if I want to have reneval email to be send, is it possible to change grace period by plan setting ? I'm afraid that email won't be send if I do that...

You would need to use CBSubs Mailer and create a mailer to sent for example 1 month before expiration date if you had a 1 month grace period.

So I've made a mistake with the terme "grace period". I thought that this period was a period untill sibscribers could benefit of rights to the reserved content but will be notified that they have to reneval their subscription. I understand it's not the case.

Grace period is time in addition to the duration that's essentially for free and is used before they will truly expire. I don't recall if expiration email trigger was ever changed to ignore grace period or not, but best way to send renewal notices is with CBSubs Mailer.