I have worked as a hospice on-call nurse, a phone triage nurse, and an intake nurse at a small hospice company, so I have fielded literally hundreds of calls from patients and their families. The big issues seem to be:
1.) the obvious one, death. Offer condolances and verbal reassurance and then go provide a death call visit. At the hospice where I was an on-call nurse, it was also standard procedure to offer a visit from the on-call social worker and/or chaplain along with my visit.
2.) pain or agitation management. "Help! I gave my dad his normal dose of Morphine and he is still moaning and crying in pain!" or, "My dad just urinated on the floor and he is trying to hit us, this has never happened before and we don't know what to do!"
Know your medication doses and, if your hospice company has standing orders for meds, know them as well, like the back of your hand, or at least have a copy of them with you handy at all times, because you will be using them over and over. You will sometimes be directing family members over the phone on how to dose pain or anti-anxiety/anti-psychotic meds, so if you can tell them that 10 mg of Roxanol = 1/2 of the syringe and they can give that much now, for example, it will help them immensely, and there are times when simply increasing med doses over the phone and making sure that the family members understand how to give them will solve the problem and keep you from making a trip in the middle of the night. However, I always made sure to tell them to call back within the hour if the meds weren't helping and if they aren't, you need to make a visit to make sure that the family is giving the meds correctly or that there isn't some other type of problem, such as the patient spitting the meds out.
3.) Fear of unfamiliar behaviors. "My mom is plucking at things in the air and talking to her grandma who has been dead for 55 years!"
Know the classic end of life behaviors so that you are able to reassure family members that things like this are normal end of life behaviors and nothing to be worried about.
4.) Family issues. "I don't know what to do. I have always taken care of Mom, and now my sister is visiting from California and she is trying to boss everyone around. I can't take it anymore!"
Know how to refer families to the other members of the IDT. For example, in a case like this, you could offer the family member the services of your hospice social worker or chaplain, and then follow through and make sure that they get a call and/or visit from that IDT member, usually the next day unless it's a real crisis. This kind of thing is not normally within a nurse's scope of practice, short of giving verbal reassurance and arranging for them to get the help of a professional trained in dysfunctional familiy issues.
5.) Be very careful of family members calling to get nursing advice about others who are not under the care of your hospice. Not that this happens a lot, but it has happened to me more than once. I had a patient's daughter call once at 2 am wanting me to direct her on what to do because her 21 year daughter had a fever and a stiff neck. She kept talking about meningitis, paralysis, etc. and was basically demanding that I tell her what to do. I told her that I was there to provide guidance for hospice patients only, and that she needed to have her daughter call her doctor and seek direction from him/her. Being a hospice on-call nurse is not the same as being "Dial-a-Nurse", and we can get in very hot water if we try to diagnose or provide direction for patients who are not under our care.
Most of all, always, ALWAYS make sure that you let patients and family members know that you are available 24/7 and are more than happy to serve them and help them with anything, that you will be awake and are expecting calls, etc., whatever it takes to reassure them that it's okay to call. I have seen families that are afraid to call after hours for fear of bothering or waking up the hospice staff, and then having horrific, sleepless nights, which is the whole reason why we have on-call hospice nurses, so that people can get the help they need 24/7. Never, EVER act like it is a chore to come out if they are requesting that you do, and always try to appear calm and reassuring, even if you feel like you don't have a clue what to do. Call your on-call supervisor if you have to, that's what they're there for.