Going even one night without sleep is not healthy and the next day you'll be feeling the effects of it and will be really tired, not alert and your head will likely hurt and you won't be able think clearly.
The longer you go without any sleep the worse your health gets and you lose alertness even more.
After 48 hours of being awake and not sleeping at all your cognitive performance will worsen, and then you will become very fatigued and after that happens your brain will start entering brief periods of complete unconsciousness, also known as microsleep.
Then if you continue to stay awake and not try to sleep after a week or two your organs such as heart, liver, brain etc can start failing and eventually death will set in where you'll go to sleep permanently and be dead.
Insomnia is rarely fatal but if you do stay up too long and go for weeks without sleep then eventually you could die and go to sleep permanently.
The insomnia if left untreated can lead to health issues such as heart disease, heart attacks etc.
When you're sleep deprived you also can get into car accidents or walk out into traffic etc or have accidents at home that could be deadly.
Because you're not thinking clearly when you're deprived of sleep.
If you suffer from insomnia and cannot get to sleep after a few nights you should speak with your doctor and get some sleeping pills.
Sometimes over the counter sleep medicines can work but sometimes people need stronger sleep medicines that a doctor can prescribe.