I will assume you are referring to John Wyndham's The Chrysalids.
In chapter five, after Sophie's toe has been discovered by Allan, the Wenders decide they must escape. David asks if he can go with them, but Mr. Wender says no:
Once they are satisfied that we are out of the district we'll be someone else's responsibility, and they'll not bother much more about us. But if Strorm were to lose his boy there'd be hue and cry for miles around, and I doubt whether we'd have a chance of getting clear. They'd have posses out everywhere looking for us. We can't afford to increase the risk to Sophie, can we?'
After it is determined that they cannot risk David coming with them, Mr. Wender asks David to stay over-night at the house even after they have escaped.
'Davie,' he said, man to man, 'I know how fond you are of Sophie. You've looked after her like a hero, but now there's one more thing you can do to help her. Will you?'
'Yes,' I told him. 'What is it, Mr Wender?'
' It's this. When we've gone don't go home at once. Will you stay here till tomorrow morning? That'll give us more time to get her safely away. Will you do that?'
'Yes,' I said, reliably.
Mr. Wender asks David to do this because he knows David will be implicated in the situation because he was with Sophie when her toe was discovered. Furthermore, Mr. Wender realizes that when David returns home, information about their escape will come to light, even though David doesn't want it to. Mr. Wender wants to delay any information about their escape being leaked so they have a chance of getting away unharmed. This concern is confirmed at the end of chapter five as David is crying in his bed after being beaten by his father saying: "'I couldn't help it, Sophie,' I sobbed, 'I couldn't help it," which informs the reader he has given information about the Wenders' escape.