Expired Filipino passport with non-expired Kuwait visa -- can I still use the visa?

The DFA has no authority to cancel or reactivate your Kuwait visa; only the Kuwait Embassy in the Philippines or the Ministry of Interior in Kuwait has the authority to do that.

The other situation where you visa gets cancelled is if you are out of the country for more than 6 months without a special exception/approval (these exceptions are provided mainly for students abroad, and in some cases for those abroad for medical procedures).

Further, there is no such thing as "reactivating" a passport. If a passport is expired, it is considered invalid for the purposes of travel - however any endorsements (like visas stamped on it) remain valid till their individual expiry date. This is why you should carry both the expired passport, and your new, valid passport if you are traveling and the visa is endorsed on the old passport.

If your visa is already stamped in the old passport (which has expired), you are free to travel with it.

Once you reach the immigration counter - they will redirect you to the administration desk, where they will stamp your old passport's visa page with a special stamp - which in Arabic means "transfer of information".

You have to go to the governorate for your company's file - and have them transfer the information from your old passport to your new passport within 30 days.

If you don't do this, your visa is effectively revoked.

If your visa is not yet stamped (and you are holding it in your hand as a visa copy), then you can also travel freely. However, I am not sure how your visa got issued in the first place as your passport should have 6 months validity for a new visa to be issued.

Finally, be warned that starting Jan 1, 2016 - the residency expiry date will be linked with the passport expiry date. So, if your passport expires before your residency (visa) expires, they are both expired automatically by the system.

This was a brand new procedure enacted to combat visa forgery and trafficking.

In general it is fairly common to have a visa which expires later than the passport it was originally inserted into. When this happens, you typically need to travel with both your old and new passports, and show both when you enter the country for which you need the visa.

You shouldn't need to do anything at your home country's office (where you got your new passport). You could contact the visa-issuing country's office to see if they recommend you get a new visa inserted in the new passport--just in case.