permesso di soggiorno (Turin)

Hi Guys,

I came from Philippines and got assigned here for work in Italy for nine months (starting February this year till November).
My work permit/contract and Visa ends this coming November. But my Residency Permit ID (permesso di soggiorno) expires till next year end of July Protected content .
I need to go back to Philippines this November when my contract and visa ends to settle some things there.
My question is, Can I still visit Italy or other schengen countries (as tourist) with just the residency permit? before that end of July Protected content .
Because i was worried of all these news regarding refugees or illegal migrant, which might affect my way in coming back here in Italy or other schengen country.
I have visited Norway, Sweden and Denmark within my tenure here, and I was planning to visit maybe other more places.

I appreciate your answers.

Thanks,
Mark