The "sin that can't be forgiven" is the blasphemy of the Ruach HaKodesh (The Holy Spirit) as it was proclaimed by Yahshua (Jesus). The other are those sins that are not repented of, for as it is written, "REPENT and THEN be baptized for the forgiveness of sin." If one refuses to repent of violations of YHWH's laws and instructions (1 John 3:4), then forgiveness is not obtainable. One must also remember that ALL SIN CEASES at death, for death is the penalty for sin, violation of YHWH's instructions (laws). She has paid and so did Yahshua.
The teachings of some "earthly" religions about "self-murder" are neither biblical nor correct, and while the destruction of the image of YHWH is not to be taken lightly, YHWH and Yahshua requested a desire for "mercy" to be weightier matters of the Law.
I would suggest you rest your mind about her taking her own life, for neither your worry nor your sorrow will change anything in that matter, but focus your energy toward living a life obedient to YHWH's instructions. Once this is, then let YHWH and Yahshua handle the rest.