Possible Clues:

• At the point of death
• Beset by dire circumstances
• One following Stipe's rockers is overcome by Dire Straits
• One nearest a certain phase of sleep is at the point of death
• One is about following eye movements, at the point of death
• Intermixes wildly as last resort
• Direly sick, distressed miner exits
• Ex-minister struggling at the last gasp
• One following rock band is at death's door
• At the last gasp I then may come over almost negligent