Is it possible/are there cases of a Saheeh (authentic) or Hasan (good) hadith having another chain which is Mursal (hadith that does not contain a Companion in the chain of narration)? What does it mean for the hadith then?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

Yes, the hadeeth may be related from a Saheeh or Hasan chain of narrators, and it has another chain of narration that is Mursal (i.e. a hadeeth narrated by a Tabi'i [successor of the Prophet's Companions]), and this Mursal hadeeth strengthens that hadeeth .

Shaykh Al-Albaani said in Irwaa’ Al-Ghaleel, when he was speaking about one of the narrators, “The chain of narrators of this hadeeth of his was classified as Hasan in Al-Fat-h. I said, ‘Al-Bayhaqi mentioned another narration that strengthens it, which is the narration of Muhammad ibn Abi Harmalah from ‘Ataa ibn Yasaar ... Al-Bayhaqi then said, 'This hadeeth is Mursal and it supports the Mawsool (having a complete chain of narration) hadeeth that was mentioned before it. Allah knows best.'’ I say: it has another narration that strengthens it and which is also Mursal.”

Shaykh Al-Albaani mentioned a number of other narrations that strengthen it, and then he said in the end, “In short, the hadeeth with these narrations that strengthen it is Saheeh.”

Allah knows best.