It is a bit counterintuitive, but in situation like this feeling safe - just a little bit - is very important. It will motivate people. Of course, nobody feels safe - not even you -, but you as a leader can do something about it.
Be positive, but not overly positive. A negative leader cannot provide a safe environment, and an overly positive leader is not credible - people are not stupid.
Share your information. When a company lets people go, there are way more questions than answers, and since information is not available people tend to fabricate answers, which are not about how the company will get up and be even better than before. They fabricate the worst things. You can manage the situation by sharing information, but let the people fill in the blanks by themselves. They'll feel safer if they are allowed to think.
Have an open door, in case they need help with the filling in. Moreover, you should start "smooth" casual conversations. Let them talk, and have a sense about what they feel. Create a "talking is safe" environment.
Do not start with new rules. It is common in life that when something happens new rules arises usually for damage control. One of the most common is "do not gossip, come talk to me first". This never works. Let people talk. If you have shared enough information, there won't be much to talk about. If your open door policy really works, there won't be much gossiping.
Keep trying, but do not be pushy. There will be hard conversations and long pauses. Do not push things, come back to a sensitive topic a bit later, or the next day.
Do not give up. Finally, you should not give up. If you do, it does not matter what you say or how you say it, people will know and it is over.