You grant a title to a petty thief? I doubt that this is in any way historical. Perhaps a peasant was pardoned if he was starving, but this would be the best result he could achieve.
Sometimes new titles were created, but they were only given to already important persons, i.e. a member who is already a member of a court in an important position.
No, only really big thieves should get titles. ;P
But I'm all for ennobling commoners and reducing poor nobles to commoner status. Your republican vassals, if you have towns as vassals, will be commoners, so there might be a way to create a "nobility of the robe" avant la lettre. And the church might be a way for upward mobility for poor people, and a noble person of either sex could gain friends, lovers, companions who are commoners, slaves, heathens.
Actually, I think it would be an interesting thing to have events for such unequal relationships, for example in realms on religious or cultural frontiers or for nobles who went on Crusade. So if the Prince of Wales returns from the Holy Land with an Arab retainer whom he insists on bringing to court with him, or the King of Sicily attends official functions with his Berber concubine on his arm (or heaven forbid if he insists on marrying her), or the Holy Roman Emperor insists on making a poor Bohemian friar his spiritual lord, over the Archbishops of Cologne, Milan, or Mainz.
The point is that you would have to defend your friendship against your nobles, with maybe negative relations with those who do not approve, maybe even events by members of your court who want to get rid of your unequal friend for your "own good"--because it is scandalous for a person of your standing to have people below your station in your inner circle, while of course you are keeping your nobles or family members out.
Some historical examples (medieval and not): Edward II of England and his Gascon companion Piers Gaveston; Carlos IV of Spain's favorite Manuel de Godoy (later "the Prince of the Peace" and the queen's lover); Rasputin; Queen Victoria's Mr. Brown. You get the idea. Could be an interesting aspect of court life and tension in your realm: unequal friends like these would be more trustworthy than the realm's magnates (they owe their place entirely on you, not lineage or inherited power) but also deceitful in trying to establish their own power base in many cases.