If one has the right to live, then one should also have the right to die. If not, then living is not a right, but a duty.

The above would match the Japanese quite well.
Is that what you're trying to say?

Russian version means something like this:
"If there is a right to life, there must be a right to death, or a right to life would be not a right, but a duty."

@CK, @sharptoothed:
Is "right on smth" an error?
Is it must be changed to "right to smth"?

2soweli_Elepanto
На сколько я знаю, "право на" переводится именно как "right to". Возможны и другие варианты, типа "title to" и т.п.
Ты не имеешь пава делать это! ~ "You're not entitled to do this!"

2CK
The current Japanese and Russian renditions mean effectively the same though they use slightly different wording, I believe. I think, it's possible to link them, nevertheless.

I slightly corrected the sentence. Does it like smootly now?

I recommend to write

"If there is a right to life, there must be a right to death too; otherwise the right to life wouldn't be a right, it would be a duty."

But of course a native speaker will be a better adviser than me.

Seems OK. But why wouldn't it be a right?