Can I Use My Current Visa Until Its Expiration While Transitioning to a New Employer in Thailand?

The following delayed me in 2015... either your employer can provide you with proof of paying tax for you, or you need to take your tax card + WP + passport to your local tax office, and pay your own tax instead, and keep the receipt. DON'T be stressed if you have to do the latter; one year here compared with back home is peanuts. :)

Not up to them to cancel your extension. It's your responsibility.

An expired work permit is not a canceled work permit. You might want to check on that status.

A fellow teacher changed schools and his previous school didn't for some reason cancel his WP. The new school was unable to get him a WP until he traveled back to the old school in a different province to take care of the matter.

It's not really an issue if you're going home or to another country but if you want to continue teaching legally in Thailand you need to get things squared away. Thailand doesn't help those that don't help themselves.

Assuming your work stopped after March 26th, you are on amnesty now and able to stay till Sept 26th. Use that time to get a new visa or plan to leave Thailand.

As it is your work permit and as it is your passport where your stay is stamped inside, you are the one responsible that it all get cancelled on the last day of working,