Steve

Steve is a guard who worked at Arkham Asylum when the Joker took over Arkham Island.

Before Arkham Asylum Incident
When Warden Sharp reopened Arkham Asylum. Steve was hired by Quincy Sharp and started working there as a security guard.

Arkham Asylum Incident
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 heard over the radio. Steve tried to reach the extraction system on the other side of the room so he could activate the ventilation system in order to filter the deadly gas out of the room, but was forced to abandon his mission and seek safety instead, scaling a ladder leading to a small utility ledge above. But then the boiler exploded, taking out Steve's ladder and leaving him hanging precariously from the ledge. The Guard turned around in desperation, spotting Batman, who landed on the ductwork behind him. He then turned and shouted at Steve, "Batman's here! Just hold on a little longer, Steve!" When further approached by Batman, the guard, without taking his eyes off Steve, begged him, "Please, you've got to save Steve." After rescuing Steve, the other Guard shouted, "Batman! The extraction system! Steve was trying to get to the control panel on the end of the room!" He repeated his message with hand gestures, then sank to one knee and sat down on the ledge. He remained there after Batman had successfully cleared the gas from the room, then, at some undisclosed time. Steve stayed in the company of the other survivors.

After Arkham Asylum Incident
Steve along with the others guards because Batman left them in a safe area so they much have surely survived the attack on Arkham and returned to his duties after the Joker was placed back in custody.

Trivia

 * Steve is a minor character that appeared in the YouTube web series The Joker Blogs.
 * There is also a guard name Steve in the beginning; it could be that they are the same person and Joker is lying to the women on the phone because Steve is saved by The Batman.