C2 point 70 in the category of FUTURE is
future perfect simple QUESTIONS:
For example:
Will they have learned that reading is a chore?
A COCA search for:
Will _P have _V*N *
This is extremely rare!
1 WILL WE HAVE LEFT 4
2 WILL WE HAVE MADE 4
3 WILL YOU HAVE TAKEN 3
4 WILL YOU HAVE LEFT 3
5 WILL YOU HAVE ACHIEVED 3
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And what will we have left?
*This example is ambiguous and might not be future perfect. ‘left’ might be functioning here as a participle/adjective as in ‘we had nothing left. There was no leftover food.’ Another rewording might be ‘What will we have that is left over?‘