The Inner Party doesn't want Winston and Julia dead as long as they are opposing Big Brother and the government. Oceania's government wants everyone to "love" Big Brother and Ingsoc, and willing to execute thought criminals only if they cease to be thought criminals. Hence, would Ingsoc consider it a failure if a thought criminal commited suicide before they could be caught? How would the Party react if they didn't get the thought criminal? E.g. if Winston and Julia had commited dual suicide, would the Party have "failed" and what would they do? Do such suicides happen in Oceania?
This is answered in the book. The Party has acted to make suicide difficult, and Winston lacks the courage to go through with it. Even so, Winston thinks there are some people who do it anyway.
From the very end of Part One
It was at night that they came for you, always at night. The proper thing was to kill yourself before they got you. Un-doubtedly some people did so. Many of the disappearances were actually suicides. But it needed desperate courage to kill yourself in a world where firearms, or any quick and certain poison, were completely unprocurable. He thought with a kind of astonishment of the biological uselessness of pain and fear, the treachery of the human body which always freezes into inertia at exactly the moment when a special effort is needed.
Later, O'Brien makes a promise:
When finally you are caught, you will get no help. We never help our members. At most, when it is absolutely necessary that someone should be silenced, we are occasionally able to smuggle a razor blade into a prisoner’s cell.
And from later after Winston has been arrested
He thought oftener of O’Brien, with a flickering hope. O’Brien might know that he had been arrested. The Brotherhood, he had said, never tried to save its members. But there was the razor blade; they would send the razor blade if they could. There would be perhaps five seconds before the guard could rush into the cell. The blade would bite into him with a sort of burning coldness, and even the fingers that held it would be cut to the bone. Everything came back to his sick body, which shrank trembling from the smallest pain. He was not certain that he would use the razor blade even if he got the chance. It was more natural to exist from moment to moment, accepting another ten minutes’ life even with the certainty that there was torture at the end of it.