My stepdaughter's mom has abondoned her!

OK so here's the deal long story but Please Read I Need Advice... my fiance and I got together when his daughter was 2 months old. He decided to end things with her mom once his daughter was born with drugs in her system(just thc not Crack or anything she's perfectly healthy) he didn't know the mom was smoking during her pregnancy. Shortly after she was born her mom was diagnosed with bipolar depression she used to text him and tell him to come pick her up or she would call cps to get her she would say things like she didn't want her anymore just crazy things to get him in her life again, that didn't work. He always tried to see her more but the mother wouldn't let him. Last straw was when she tried to commit suicide while her kids were present she has an older son who is not my fiancé . He immediately went and filed for emergency custody which was granted!! That was 2013. She was 18months that's when I became more of a mother figure to her, her mom went through classes to get her back but only on the weekends. Once she turned 3 and my fiance got full permanent custody of her she has been completely absent no phone calls no visits no support or anything she is now 4. we refuse to hunt her down for child support plus she gets social security because her bipolar so we wouldn't get much anyway.

My thing is should we seek to terminate her rights as a mom it's been over a year and no contact, she knows me as her mommy and knows her mom only by her first name this has been like that for almost 2 years now. I'm afraid one day she'll just come out of the blue and want her back! I check her Facebook every now and then she has another son now and married it seems like she's just moved on but I don't see how a mother could do that. Should we leave things the way they are or terminate rights so I can adopt her after we're married?? Any advice is helpful! !