Can I leave Thailand and re-enter on a 30-day exemption if my non-immigrant B visa extension expires?

Hi! I am currently on a non-immigrant B visa that I extend every 3 months through my work. At the beginning of June my extension will end and will need to apply again but it will not be possible as I will not be under my current company anymore and I need to stay another month. Can I go out of the country on the day of the expiry of the extension and come back 2 days after with 30 days visa exoneration (as an Italian citizen)? Does my company need to cancel my visa (the working visa still exists even though the extension will expire) and work permit before being able to come back without a visa?