Differing generation systems have different minimums for each "rolled" stat, before modifiers are applied. In the standard, classic, and dice pool methods, the minimum is 3. In the heroic method, the minimum is 8. In the purchase method, the minimum is 7.
There are a lot of modifiers one might accrue during character creation, and some of them are negative.
Strength can be lowered, among other things, by venerable age and being a gnome, which is sufficient to reduce even the heroic method's minimum to 0.
Dexterity can be lowered, among other things, by being a venerable syrinx, which is sufficient to reduce even the heroic method's minimum to 0.
Constitution can be lowered, among other things, by venerable age and being an elf, which is sufficient to reduce even the heroic method's minimum to 0.
Intelligence can be lowered by being a Trox, and by the Accelerated Affliction manifestation of the Plagued Corruption corruption. It seems there are no other permanent intelligence penalties combinative with race available at level 1, at present. This makes the minimum intelligence score for the rolled non-heroic systems 0, while the minimum for the purchased system would be 3, and the heroic system 4.
Wisdom can be lowered, among other things, by being young, being a Trox, being a steelbound fighter with a cool bonded weapon, and possessing a severe addiction. These are sufficient to lower one's Wisdom score to 0, even in the heroic case.
Charisma can be lowered, among other things, by being a Trox, the Gnashing Bite manifestation of the Ghoul corruption, the Transformed Flesh manifestation of the Hive corruption, and the Accelerated Affliction manifestation of the Plagued Corruption corruption. These are sufficient to lower one's Charisma score to 0, even in the heroic case.
The lowest most scores, neglecting generation constraints, can be when creating a character is 0, but some scores can't be lower than 1. This is because the minimum value for any ability score is generally taken to be 0, and reaching 0 in each score has special effects. If those effects would result in a dead character, the character would start play as a petitioner rather than a member of their chosen race/age/etc and thus would have much higher stats. That's why scores whose special effect on dropping to 0 is death can't go lower than 1 in character creation. If abilities are allowed to become truly negative (there is no strict prohibition against this), then scores that can be 0 can generally be reduced at least a little more, but we're not going to address that here.
A character with a Strength score of 0 is too weak to move in any way and is unconscious, but is not dead, and thus is a valid choice for a starting character.
A character with a Dexterity score of 0 is incapable of moving and is effectively immobile (but not unconscious). Such a character is not only not dead, but may well still be able to affect the world in meaningful ways and serve fairly well as a starting PC.
A character with a Constitution score of 0 is dead. This means that really a starting PC can't have less than 1 Constitution.
A character with an Intelligence score of 0 is 'comatose', which is not otherwise defined in the rules. It probably means they are supposed to have the unconscious condition, but we can't really be sure. In any case, they aren't dead (unless your GM decides that beings move on to the afterlife when medically dead rather than biologically dead, and that int 0 comatosea is a form of medical death). In any case, this is largely academic since you can't reach a score of 0 in the purchased system in character generation.
A character with a Wisdom score of 0 is incapable of rational thought and unconcious. Such a creature is not dead, subject to the same caveats as Intelligence, and thus is an acceptable starting PC.
A character with a Charisma score of 0 is not able to exert himself in any way and is unconscious. Such a creature is not dead, and thus is an acceptable starting PC.
This means, in sum, the minimmum ability scores after acounting for modifiers in the purchased system are as follows: