Names can't be redrawn in a Wishpicks Secret Santa, but the organizer can still add or remove people, and others can leave; each change moves two names at most.

Only the people whose person changes are told, and everyone else keeps theirs. For how a group runs from the invitation to gift day, see "How does Secret Santa work?".

Yes, if the organizer lets them in. Once names are drawn, the link shows Ask to join instead, and joining still needs a Wishpicks account. The organizer sees the request under Waiting to join and taps Add to the draw or Decline; adding someone gives one person a new name to buy for. While you wait, the group's page shows the last day you can be added, and you can tap Withdraw request if you change your mind. Someone who left or was removed before the draw and opens the link again waits for the organizer too.

Anyone but the organizer can tap Leave this group, and the organizer can tap Remove next to someone's name. Before the draw, nobody else is affected. After it, while changes are open, one or two people get a new name to buy for, and only they are told: "You're buying for someone new". If that's you, your reservations on the previous person's list are cancelled so someone else can reserve those wishes, and a gift you already bought is yours to keep for your new person or return.

If you leave after the draw before your gift is given, what you reserved for your person is cancelled. Your own list shows what's reserved on it again, but never who reserved it while you were in the group. To come back, you'd have to ask to join again. If the organizer removes you, you get a notice in Updates saying you're no longer in the group, with no reason and no email, and the group no longer opens for you.

Three times in all: people can be added, removed or leave until a few days before gift day. When the organizer adds or removes someone, the confirm screen says how many times are left, and once the first change is made, the organizer's group page also shows how many remain and the last day for them.

If someone leaves or is removed and the group's rules leave no way to move names, no name moves, and after that nobody can be added and no names move again; the confirm screen warns first when that can happen. Once changes are used up or closed, people can still leave or be removed, but no names move: someone in the group may be asked to step in for the person the leaver was buying for.

While changes are open, you get a new person instead, unless the group's rules leave no way to move names. Otherwise the group's page says "Your person left the group": you're no longer buying for anyone in this draw, and a gift you already bought is yours to keep or return. You may be asked to step in for someone else, and any request appears on the group's page.

From the day after gift day, open the group and tap Nothing arrived. Your Santa is told, and reporting it doesn't reveal who they are. Usually they have 14 days to say the gift is on its way before others may be asked to help. The group closes about a month after gift day: if that wait would leave less than 24 hours before closure, help may be offered immediately. People whose own gift is ready may be asked to give one more gift inside the budget; someone accepting or delivering a gift before closure isn't guaranteed. If your Santa marks it Given before anyone steps in, your report closes. If the gift turns up after all, tap It arrived after all, or Cancel my report to take it back.

The ask shows the budget and, while gift day hasn't passed, the day to give by, and says others may be asked too; you see who it's for and their list only once you tap I’ll do it. Open them from the group's page: you get their list, or gift ideas inside the budget if they have none. Tap Given there once you've given the gift. Only you see that mark, and nothing about it reaches the person you're helping.