There are situations where your village is doom to a certain death. Here are some of those scenarios, how to avoid them and eventually solve the problem.

Only males/Only females/ Only one remaining villager
If you have only picked males or females at the beginning of the game, or if all of your female/male villagers have died, your game is basically over because you won't be able to have children and continue. Your remaining villagers will die of aging eventually and your game will end there. Before resetting your game, here's what you can try:

At the marketplace, you can purchase 1 male 1 female and a child to save your village, if you have 200 lavastones.
Wait for a special event to occur. Sometimes a special event will bring new members to your tribe, but there's a chance they have the same gender than the rest of your village.

Only children
If all of your adults died, you're in a tough situation because none of the remaining children will be able to work until they are 14. You can try providing food by foraging a lot of mushrooms, it will be your only way to gain food.

No more food
The coconut tree is NOT a limitless source of food and will run out of fruit eventually. Once your coconut tree stopped providing fruits, you will have to wait a long time for new fruits to grow. What you can do:

Don't have too many farmers. One is enough to begin the game.
Purchase Farming tech as soon as you can, once you've unlocked fishing, you'll have an unlimited source of food and it won't be a problem anymore
Don't forget to forage mushroom to have extra foods
Don't make too many children till you've unlocked the unlimited source of food
Some special events can occur where you will either gain food, or the coconut tree will provide fruits once more. But the opposite can occurs as well: your food bin might end up empty, or the coconut tree can stop growing fruits.

Everybody is sick:
It's not the end, even if you don't have any doctor. Chose one villager and drop it on another villager until he's healed, and repeat the process until everybody is healed.

Lit the fire, it will avoid sickness in the future.
If your villagers have low health, drop them on the food bin: eating will restore their health.
Some potions can also restore health
Improving Medicine tech can help avoid that problem in the future.
Train someone to be a doctor, so that they will automatically heal the sick villagers
Diseases can be spread. Make sure everyone is healed before quitting the game.

Time travel:
Time travel is tempting, but if badly used, all the tribe can die instantly either of starvation, aging, or sickness. Before you timetravel, make sure you:

Have an unlimited source of food, and farmers
That the fire is lit, and that you have a doctor so that your villagers don't die of sickness.
If you plan to make a really long time travel, have several villagers with auto breeding on, so that they don't die of aging

Deaths causes:

Knowing the causes of death can help you avoiding them
If there's no more food, your villagers will die of starvation
Aging: the health of your villager will slowly decrease with age till the death of the villager. This cannot be avoided but slowed down by improving Medicine tech
Sickness: if a villager is not healed, his health bar will decrease. The villager will die when his health bar as reached 0
Accidents: In previous games, if a potion making went wrong, an explosion could occur and seriously damage the health bar of a villager. If the health bar is already low during the explosion, the villager will instantly die.
Wrong potions: some potions will make a villager sick, or decrease his health bar.
Special events: special events can cause a villager's death. This cannot be avoided.