I would like to know if someone is unable to sign their signuture can next of kin do so?

Only if that relative has power of attorney. Otherwise, the relative's signing is illegal.

If that person can not write their signuture can next of kin write a letter on someone be half and sign his own signuture?

The relative can write a letter on behalf of the person unable to sign, but the signature at the end of the letter must be that of the relative who wrote the letter.

If someone is unable sign their name can next of kin sign their own signuture,is that excaptable?

I already answered that. It is illegal and unacceptable for someone to sign for next of kin who cannot sign his/her own signature. The ONLY exception is if that someone has power of attorney for the other person.

Would the counsel excapt a letter by next of kin

Would the counsel excapt a letter by next of kin

A letter saying what, for what?

If the next of kin has been granted a power of attorney on behalf of the incapacitated person, then yes.