Warning, don't fry your modem.
Some years ago, an EMT vehicle backed over and destroyed my Hughes dish. The next morning I called my trusty tech company, and the first thing he asked me was if the coax was damaged, and next if had I cut the power to the modem.
I didn't discover that the coax was broken until the next morning, and I hadn't powered down the modem for all of that time. He said that with all the rain we had that night, that the modem was probably fried, so he would make sure that the tech he sent brought a new modem with him, and for me to unplug the modem at once, even though it was probably too late by now.
He was right, the modem was fried.
I knew that coax was designed to carry extremely weak signals, and I didn't think there was enough power available to cause any damage. Looking back now, I think it was probably the transmit signal to the dish that probably had enough power to do the damage, and the water on the broken end of the coax caused a short on the transmit circuit of the modem. At least, that's my theory.
I suspect that this may be true for the newer generation modems also. I'm going to play it safe from now on, and if anything ever happens to my dish again, I'm going to immediately cut the power to the modem.
PREJUDICE, n. A vagrant opinion without visible means of support.
The Devil's Dictionary
Yes, there is DC power supplied by the modem going through the coax to power the radio on the dish. Under certain situations the modem can be damaged if the power is shorted out. There are protections built in but they don't always work.
Also one reason we say to power down the modem from the wall receptacle, not the plug on the back of the modem.