If a person truly "has faith in Christ" then they will follow His teachings.People who kill themselves do so because their minds are consumed with hatred;hatred of themselves,others who have harmed them and sometimes of God who they blame for not resolving their problems for them.
The "thou shalt not kill " commandment is usually quoted to counter suicidal impulses but more meaningful is Jesus' teaching on love and forgiveness which should be applied to all enemies,both personal and global:
Luke 6:27 (New King James Version)
“But I say to you who hear: Love your enemies, do good to those who hate you,
(which include you yourself)
For those who insist in ending their life in a mad fit of rage and forgiveness, then these verses will apply:
Galatians 5:19-21 (New King James Version)
19 Now the works of the flesh are evident, which are: adultery, fornication, uncleanness, lewdness, 20 idolatry, sorcery, hatred, contentions, jealousies, outbursts of wrath, selfish ambitions, dissensions, heresies, 21 envy, murders, drunkenness, revelries, and the like; of which I tell you beforehand, just as I also told you in time past, that those who practice such things will not inherit the kingdom of God.
Mark 11:25-26 (New King James Version)
25 “And whenever you stand praying, if you have anything against anyone, forgive him, that your Father in heaven may also forgive you your trespasses. 26 But if you do not forgive, neither will your Father in heaven forgive your trespasses.”