I will stick with Guillotine as the example game, but the issues here apply to most games.
If the rules of a game tell you to do something, purposefully "forgetting" to is cheating. Thus 1b is an easy NO.
1a is a much harder question. Tl;dr: In casual play, have your group agree on something; in tournament play, call a referee or refer to your game's tournament guidelines if they exist.
Some issues involved are:
- If you don't allow the draw, you are 1) willfully preventing an action mandated by the game and 2) punishing them for what's probably an innocent mistake.
- If you do allow the draw, you are making it easier for them to gain advantage (on purpose or by accident) by 1) drawing on turn, then saying they forgot and drawing again or 2) changing opponents' thoughts and actions by temporarily having one fewer card.
Here's a few example cases.
Case 1 - You're all friends trying to have fun. Then whatever you can agree on goes; here are a couple possibilities:
- Case 1.0 - Bob starts a turn. Alice says she forgot to draw. Bob says he's ok with Alice drawing and Claire concurs, so Alice draws (and is told to be more careful).
- Case 1.1 - Bob plays the swap hands card on Claire. Now Alice says she forgot to draw. Bob says he would have wanted Alice's hand had it had one more card in it. By now he's seen Claire's hand though, so swapping for Alice's instead would cause an even bigger disruption to fair play. Thus he suggests that Alice has benefitted from not drawing and should not also get the benefit of drawing afterwards, and all agree.
Case 2 - Winning this game is really important to you, and/or you don't trust your opponent. Then know before the game how disputes will be settled!
- Case 2.0 - There's a judge/referee; go ask them.
- Case 2.1 - There's a tournament procedure guide (not in Guillotine though, to my knowledge). For example, the MtG folks have an Infraction Procedure Guide ( https://www.wizards.com/ContentResources/Wizards/WPN/Main/Documents/Magic_The_Gathering_Infraction_Procedure_Guide_PDF1.pdf) where they lay out in insane detail everything that could possibly go wrong in a game of Magic and what to do about it. Failure to draw would probably fall under the generic "2.5. Game Play Error — Game Rule Violation"; the player would get to draw but would be issued a Warning (getting multiple Warnings can cause you to lose the game). [I've played in circles where, when an arbitrary game does not have the rules clarification we're looking for, finding the most relevant rule/procedure from MtG is an accepted way of settling disputes.]
- Case 2.2 - It's just you, a stranger, and your $100 dollar bet on the outcome. I'm sorry but this was a really bad idea.