Deacon Greg asks this important question...and gives this example from the Washington Post
"He said 'I'm a dying man, and I want to see a priest,'" Mary Baus remembered. "All they said was that they didn't have one."
Baus survived, but his wife said it was a traumatic event that left both her and her husband shaken.
"There used to be a chaplain available if you needed him," she said. "Or you could get a priest to come to the hospital. Now it's not for sure that you will see anyone."
Finding a priest to be at the bedside of the dying is becoming harder and harder across the country. The shortage of priests has been a problem for years, but its implications become most clear at dire times for the ill.
I agree with Deacon Greg who says that Deacons would be great here to use as ministers of the sacrament. My thought is perhaps even a new clerical position intentionally called "chaplain" that could administer anointing of the sick and the Eucharist only--a bet a lot of Catholic doctors would sign up.
It's an important position. I remember when I worked in Calvary Hospital as a volunteer with pastoral care, all people really wanted was someone to talk to and someone who could pray with them in their dark moments. It would have been great to have some kind of ritual that we could have done together on a regular basis at a moment's notice or to be able to administer the anointing of the sick. I'm sure it's a question that will come up at the med school with me often. It's going to take the laity to really speak up about this.
So what are you waiting for? Start writing your letters to the local bishop or to the USCCB.