User blog comment:B214/General Discussion/@comment-3965848-20170408140058/@comment-29963364-20170408185827

Stray Devils are those who have "strayed" from their masters (Kings), either by running away, or killing them.

There are two reasons why the Devil Society tracks and kills these strays:

1.) Without their masters (Kings) to keep them in line, they are likely to give in to their "more chaotic & destructive" desires and cause irreparable damage for the Devils.

2.) The Devil Society needs to "set an example" for all the other Reincarnated Devils who might be thinking of doing the same thing.

I'm sure you remember what Ajuka said about Issei's Evil Pieces needing to be adjusted because Issei's power had increased so much in too short a time, and the Evil Pieces couldn't keep up? Maybe this is a hint as to how/why some Stray Devils take on more monstrous appearances. Their powers & abilities become too much for their Evil Piece(s) to handle, and the "negative effects" cause their minds and bodies to morph/deteriorate/distort in some way, similar to how [Chaos Drive] causes Sacred Gear and Holy/Demon Sword wielders to change as well.

As for how Kuroka doesn't change, remember that her master (King) had been conducting experiments with his servants on how he can "make" them power-up. Eventually Kuroka's powers & abilities became so strong that she out-classed her master, then killed him to protect Koneko (Shirone).

Perhaps Kuroka new that increasing her power by too much too fast would have "negative effects", so she decided to slowly, but effectively, get stronger during her time as a Stray Devil. But since she was already High/Ultimate-Class when she killed her master and became a Stray Devil, she probably didn't need to power-up that much.