Learn Finnish: Toimitusjohtaja ei irtisanone kaikkia työntekijöitä. - The CEO probably won't lay off all the employees.

To form the negative potential, you use the conjugated negative verb (here ei for the third-person singular) followed by the potential connegative stem of the main verb. For a Type 1 verb like irtisanoa, you take the strong vowel stem (irtisano-) and add the potential marker -ne. Because it is a negative sentence, no personal endings are added to irtisanone.

How does the meaning change when the potential mood is made negative?

The potential mood expresses that an action is likely or probable, but not absolutely certain. When paired with the negative verb, it simply negates that likelihood. So while irtisanonee means "probably will lay off", ei irtisanone means "probably won't lay off" or "is unlikely to lay off".

Why is the object kaikkia työntekijöitä in the partitive plural?

This is due to the standard Finnish rule for negative sentences: if the action of the verb is negative, the object must be in the partitive case. Because the CEO probably won't lay them off, the object "all employees" takes the partitive plural form kaikkia työntekijöitä.

If this sentence were affirmative ("The CEO probably will lay off all the employees"), how would it look?

It would be: Toimitusjohtaja irtisanonee kaikki työntekijät. The verb gets the third-person singular ending, which lengthens the final vowel of the potential marker (-ne becomes -nee). Additionally, because the sentence is no longer negative, the object changes from the partitive plural to the accusative (which looks like the nominative plural for standard plural objects).