Nothing occurs that isn't either caused or allowed by God. If it happens, He could have stopped it from happening. Since it did happen, then God either caused it or allowed it. Because God is righteous, loving, gracious, powerful, and wise, then He can be trusted with what He allows or causes. He's got some good reason for it, including sickness.
Most people get over most sickness. Men recover from sickness much more than they retain it. Again and again God either causes or allows someone to recuperate from a sickness. We should expect it. Many more times than not, men get better. I have witnessed men to survive many more situations where they should not have survived, then dying when they might have survived. Men survive at an astounding rate in comparison to what could have occurred.
When someone dies of a sickness, God could have stopped it. He didn't. Since He didn't, He must have had a good reason not to have terminated it. God would be justified in either allowing or causing any sickness for anyone. Since we know God is in charge, we also know that God has done what is best. A believer will rejoice in that and live with contentment in whatever God chooses to do or allow. God is going to work everything toward the best. The recognition and acceptance of God's perfect attributes trusts His providence.
Even if someone dies, if He is saved, He has died unto the Lord. God might not keep someone alive. Believers should not be so preoccupied with this earthly life. They should look forward to their heavenly home and its fellowship with God. This isn't fatalism, where someone gives up on life. This is when someone does his best to prevent his own death, but also finds the prospects of death acceptable.
To express the above in a personal way, when I'm sick, I thank God for His goodness that He has caused or allowed me to live this long. I acknowledge my acquiescence to whatever His plan. I know God will do what is right. This is not my rejection of living the best I can as long as I'm allowed. God will either heal me or allow me to be healed if He wants. I do all that I can or should do to stay alive and leave the outcome to the Lord. With faith in Him, I please Him.
I expect to get over a cold or a flu, because that's the way God operates. If I were not to get over a cold or a flu and I died from one of the two, I would know that is the good, righteous, and wise plan of God. So far, I've survived all my sicknesses up to the age of 53. What I believe is that what I've received is far more than what I deserve. If someone else gets sick, I encourage them in the providence of God. I pray for them spiritually to trust in the Lord and grow from the experience. Like the Apostle Paul, I don't see living in such circumstances to be superior to dying, even if I wish someone to live.
If I want to live longer, I believe I can affect that outcome with diet and exercise. If I choose to eat in an unhealthy manner, I don't expect God to intervene despite the poor decisions I've made. I deserve what I get. That goes for others as well. I understand how that someone who smokes for a few decades might die from a smoking related sickness. Again, we should trust God's providence.
Paul wrote that godliness and contentment are great gain. Contentment relates to the providence of God. Contentment also relates to our physical conditions. If we live godly, we are content with whatever state we are. If we live, we live unto the Lord. If we die, we die unto the Lord.