I have a D-2 single-entry visa and my ARC is still being processed?

This needs to be handled carefully, because the single-entry detail is the key issue. A single-entry visa is generally used up the moment you leave Korea, meaning the visa itself will not let you back in, and the re-entry permit that normally allows you to return is tied to having your ARC issued. Since your ARC is still being processed and not yet in hand, leaving now creates a real risk that you cannot simply fly back on the same visa, so please do not just depart without checking first.

Even in a genuine family emergency there are options, but you need a definitive answer before booking. Contact immigration urgently through the 1345 hotline and press for English, or call or visit your local immigration office, explain the emergency, and ask specifically about your re-entry situation given that the ARC is pending. Depending on your case they may advise on a re-entry permit, the timing of your ARC issuance, or what visa you would need to come back. Also tell your university's international student office immediately, since they handle these situations often and can coordinate with immigration on your behalf and help protect your enrollment. Keep all documentation of the emergency. The core point is that leaving on a single-entry visa before your ARC is issued can jeopardize your return, so get immigration's confirmation before you commit to the flight if there is any way to do so.