The only mention of Steve's name that you heard at the Asylum was when Batman was following Frank Boles' trail by using the alcohol traces in the air. As he passed a phone, it started ringing, and a female relation of Steve (possibly his wife or girlfriend) called to check whether Steve was alright. The Joker answered the call, and said that's going to take a minute. A few seconds later, he called back, and claimed that he could only find Steve's head, while he said 'I'll contact you when I find the rest of him!', and ended the call with his usual maniacal laughter.
When the Joker answered the call, he implied that Steve was dead. That was unknown, although it was highly likely. One possible theory for his survival, however, was that the Joker displayed his twisted sense of humor, and was lying - or as he would put it, 'joking'.
Steve was a minor character that appeared in the YouTube web series The Joker Blogs.