Speed Reduction Mid-Movement?

[Wolfswift]

So, I have an ability from third party that gives me an icy aura causing those who enter it must make a fort save or reduce their movement speed, (among other less relevant things) but if that reduces their movement enough that they've already moved their newly adjusted speed or more, are they forced to stop? I tried looking this up, figuring people'd be discussing readying an action to cast slow or something would come up, but nothing. I thought of discussions of caltrops would solve this, but they specifically say those who are running or charging stop and don't otherwise cover this.

[Biggus]

if that reduces their movement enough that they've already moved their newly adjusted speed or more, are they forced to stop?

I don't know of a rule which specifies this, but it doesn't make sense that they would. Your speed is a speed, not a distance; 30ft per round is another way of saying 5ft per second or 3.4mph. So if it halved your speed (for example), you'd then continue at 15ft per round (5ft per 2 seconds, 1.7mph) for the rest of your movement. Otherwise it's not halving your speed, it's making you stop.

[Sneak Dog]

For actions if you get a condition mid-turn it applies immediately. If start a full attack and get staggered after two attacks for whatever reason, your full-attack ends right there. Presumably the same applies here. Your movement restriction applies immediately and if you already moved more than your new speed, you stop moving.

https://paizo.com/paizo/faq/v5748nruor1fm#v5748eaic9rb0

[Darg]

So, I have an ability from third party that gives me an icy aura causing those who enter it must make a fort save or reduce their movement speed, (among other less relevant things) but if that reduces their movement enough that they've already moved their newly adjusted speed or more, are they forced to stop? I tried looking this up, figuring people'd be discussing readying an action to cast slow or something would come up, but nothing. I thought of discussions of caltrops would solve this, but they specifically say those who are running or charging stop and don't otherwise cover this.

It would work just like difficult terrain. They would enter the space, but if they failed the check it would have cost them x extra movement. So let's say the creature has 30 speed and the half speed aura starts 15 ft out. The creature moves 20 ft to enter the aura, but the aura starts at the boundary so when they fail the check that last 5 ft costs them 10 ft of movement leaving them with just 5 ft of movement left. From here they have two options: use the 5 ft to leave the aura, or stay where they are at because they don't have the 10 ft to move another square forward. Now, just like difficult terrain if the character would have only had 5 ft left to enter the aura, the check determines whether the character can actually enter the area.