Moral dilemmas and temptations, failures and mistakes, loss of control, power struggles, ego-related conflict

It's a sad fact of human nature that people don't always feel remorse for wrongdoing; very often, they only express regret for getting caught. When a character trying to keep their actions secret discovers that someone knows about their behavior, they may experience conflict in the form of what to do about the witness.

The character being caught in the act of doing something wrong
Realizing a security camera may have recorded the character's misbehavior
Receiving an anonymous email or text from someone claiming to have witnessed the act
The character seeing someone in the vicinity who may have witnessed the act
Being confronted by someone who witnessed the misbehavior
Being blackmailed by someone with details about the event
Someone asking specific questions that indicate they already know the answers

Being confronted by the witness
Feeling embarrassed about being caught or guilty about the wrongdoing 
Needing to convince the person they didn't see what they thought they did
Having to quickly manufacture a convincing cover story 
Having to do favors for the witness to prevent them from telling anyone
Not knowing what exactly the person saw or heard
Living on pins and needles; constantly expecting to be confronted and accused
Spending time doing damage control
Having to surveil the witness to see who they talk to 
Investigating the witness to find leverage that can be held over them if needed
Having to falsify evidence or secure an alibi (in case the witness speaks out)
The witness telling someone else—meaning more people the character must neutralize
Trouble sleeping and eating
Being distracted at work or school
Having to lie convincingly by remaining calm, controlling one's body language, and speaking in an unrushed and unconcerned tone
Having to figure out what the witness knows and if anything should be done