Are sentences 1 and 2 correct:
1-This is the box whose reason for being here is that someone forgot to throw it out.
(This is the box that is here because someone forgot to throw it out.)
It seems to me that 'whose reason for being here' doesn't work here. It is as if we are talking about the motive the box had to be here.
2-This is the man whose reason for being in prison is that he got caught robbing a bank.
(This is the man who is in prison because he got caught robbing a bank.)
Again here I feel that the sentence doesn't work because 'whose reason for being in prison' seems to imply that he intended to go to jail.
In both cases I would reword:
The reason for this box being here is that....
The reason for this man being in prison is that...
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