It is taught that ending 'e' or whole syllable is silent in speech. But I've noticed that some singers kinda reserve a space for it (pause for a rhythm beat) and sometimes give it subtle or half realization. Is it my illusion, the singers' specifics, or common practice?
No, it's common practice. Sometimes even words that don't end with e have a long "eu" sound (mostly in children's songs)
See these examples:
Nursery rhymes with frequent and strong "eu" sounds at the end of verses.
"Adult" song with "eu" sounds in the chorus. In this one the "eu" is sung in a different note than the rest of the word.