If the affected permanent gains an ability after Unable to Scream becomes attached to it, it will keep that ability.

Unable to Scream's second ability overwrites all previous effects that set the creature's base power and toughness to specific values. Any power- or toughness-setting effects that start to apply afterward will overwrite this effect.

Effects that modify a creature's power and toughness, such as the effect of Jump Scare, will apply to that creature no matter when they started to take effect. The same is true for any counters that change its power and/or toughness and effects that switch its power and toughness.