This is how Martha Stewart was imprisoned. The securities fraud charges could not be substantiated and were thrown out, so they continued her case on, among other "meta"-crimes, making false statements to a federal agent.

Moreover, since she lied to SEC investigators involved in her case, prosecutors could easily tack on an obstruction charge. And since her business partners lied as well, a conspiracy charge was on the table.

If you don't speak, you cannot lie.