Negative intelligence reduces the starting skills
The wording used by classes for your trained skills isn't unique, for example the same wording is used a lot in Chapter 1 of the CRB:
Your character’s Perception modifier measures how alert they are. This modifier is equal to their proficiency bonus in Perception plus their Wisdom modifier. For more about Perception, see page 448.
On page 448 the corresponding check is explained in full and we can see that 'plus' is literally '+':
Perception check result = d20 roll + Wisdom modifier + proficiency bonus + other bonuses + penalties
So if your class states something like:
Trained in a number of skills equal to 4 plus your Intelligence modifier
Then you do a proper addition, even if the modifier is -1:
number of trained skills = 4 + Intelligence modifier = 4 + (-1) = 3.
The defining feature of a modifier is that it can be either positive or negative. This is just mentioned in passing in Step 1 for checks:
You’ll then identify all the relevant modifiers, bonuses, and penalties that apply to the roll. A modifier can be either positive or negative, but a bonus is always positive, and a penalty is always negative.
If we were meant to ignore negative modifiers by default, then the notion of a modifier just wouldn't exist in the rules and every modifier would be a bonus instead. That clearly isn't the case, so in general we need to account for the negative modifiers, unless we are explicitly told otherwise (i.e. the languages, as you've already noticed).