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Is it possible to have negative stats in battle? Or the minimum is 1 or 0?

Example - Shuckle at level 1 with Sassy Nature (-Speed +Sp.Def) with -6 speed and paralyze.

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No, It isn't.
I am SO sure that this is straight out of demat's profile >.>

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All Pokemon have what are called stats. At the bottom of this picture with Landorus's information, you can see his base stats.

enter image description here

Base stats cannot have a negative number. The lowest they can be is 1.

However in battle, if a Pokemon receives a stat drop or raise, then it's stat stage will become either more powerful, or weaker. These are known as stat stage modifiers and only last the duration of the battle, until the Pokemon is switched out, or a move such as Clear Smog or Haze is used.

Moves such as Leer, Sticky Web, and Growl all cause stat stage drops. Abilities like Gooey and Intimidate also cause stat stage drops. A stat cannot be lowered past -6.

Moves that raise stat stage such as Swords Dance, Dragon Dance, or Amnesia raise the stat stage of the affected Pokemon. Abilities such as Defiant and Competitive also raise stat stage. Stat stage cannot be raised past +6.

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Here is a chart with all of the stat modifiers for Attack, Defense, Special Attack, Special Defense and Speed.
http://i.imgur.com/MRhqlRs.png?2
Your answer is misleading; it conflates base stats and in-battle stats. They are not the same thing. The screenshot shows Landorus's base stats, but base stats cannot be raised or lowered, and the fact base stats cannot be lower than 1 does not logically imply that in-battle stats can't be.
Actually, he pretty clearly explained it.
**However in battle**, if a Pokemon receives a stat drop or raise, then it's stat will become either more powerful, or weaker.
There is no earthly way someone who does not already know that in-battle stats are a separate entity would deduce that the word "stats" refers to two completely different things in this answer simply based on the words "However in battle". Showing a screenshot of base stats, calling them "stats", and then saying "stats" can become higher or lower in battle just implies that base stats are the same as in-battle stats and can be changed in battle, not that there's a whole separate thing calculated from base stats and several other things with a mathematical formula that can be changed in battle.

I get what MrKijani was trying to say here, but I fear it would completely confuse someone who doesn't already understand these concepts.
It is correct that I did not directly define the stats properly.
2 votes

No, it is not possible for a stat to be negative.

The lowest a Pokémon stat can be is 1. Any time a stat would be lowered to zero, it will be made 1 instead.

Note that a stat stage of -6 does not mean that 6 is subtracted from the stat; it means the value of the stat is multiplied by 2/8, or 0.25 (you can find more information on how stat stages work here). There is no in-battle effect that adds to or subtracts from a stat, only effects that multiply or divide them. So even if stats could be zero, it would still be impossible for them to be negative, simply because taking a positive number and multiplying or dividing it by another positive number will always give you a positive number.

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"even if stats could be zero"
They can't be zero at all. The lowest base stat is 1 (Shedinja) and as you said all stat stage modifiers within battle are multiplication and division and the only way to get 0 via multiplication and division is by multiplying or dividing by 0.
I know they can't be zero at all; that's why I said "The lowest a Pokémon stat can be is 1. Any time a stat would be lowered to zero, it will be made 1 instead." It's a hypothetical statement, hence the "even if they could".

That being said, you seem somewhat confused on why that is - it has nothing to do with base stats, and while your math is correct for the real numbers, the games round everything down to an integer, which would hypothetically make a stat of zero possible. For example, if you had a Speed stat of 1 and then became paralyzed, the result would be rounded down to 0 (you can't have 0.25 Speed). However, every time a stat is lowered, the game checks if the result is zero, and if it is, it immediately sets the stat to 1 instead - hence "Any time a stat would be lowered to zero, it will be made 1 instead."