Okay, I know what you are thinking. Living constructs are warforged, right? Well you would be half right, warforged are living constructs. So are the 4th Edition race, shardminds, which are living crystal beings. Neither race existed when the Scarred Lands were put into print, and yet there is a good case for including them among the people of Scarn.
Most living constructs would live in Termania. In Virduk's Promise we have many reports of strange constructs traveling the land, and even occasionally adding travellers who are in trouble. Some claim that these golem-like creatures are creations of Golthagga the Forger while others claim that they are creations and emissaries of Trelu, demigod of form and reason. Regardless of who created these mysterious beings, they make a great way to introduce the warforged into the Scarred Lands.
Let us assume for a moment that they are creations of Trelu. There are two ways that they could be dealt with. The first way is that they are prototypes of Corean's Hollow Knights and that Corean worked with Trelu to create the animated paladins. In this scenario the warforged are few in number and generally do not congregate in large numbers. They are aware that they are a rough draft and many may become embittered towards the divine powers.
The second scenario is that Trelu saw the Hollow Knights and decided to improve on them. There are two flaws with the Hollow Knights, 1) they are not truely alive, and 2) more of them cannot be made. Trelu wanted to create a race that is the perfect embodiment of form and creativity. In this scenario the warforged have their own culture and society that exists in hidden cities and they are as dedicated to the gods as any other divine race.
Shardminds also can have a home in Termania. The Tepuji in the Gamulganjus Jungle are filled with arcane crystals that have a number of strange properties. The shardminds were first born when Mesos was destroyed by the gods. Instead of dying, his titanic essence was absorbed by these crystals. These beings have none of Mesos's memories but they do have his talent for arcane power. It has since been discovered that shardminds can "grow" new members of their own race the same way that new crystals grow from existing ones. Each new shardmind that is born spreads Mesos's essence even thinner and yet conversely makes him even less likely to be destroyed. Ironically, most shardminds are dedicated followers of the gods despite being the literal embodiments of one of the Titans.
The last option for living constructs is the previously mentioned Hollow Knights. Let's be honest, nobody had thought of living constructs when the Creature Compendium was first published with the Hollow Knight in it. However, given the background and fluff of the Hollow Knights as paladins of Corean who were given construct bodies after their death and then stuck in that form when Vangal double crossed Corean; it seems like the living construct type would be more likely to be used in creating them today. There are three ways to deal with this. One is just to go with things as they are. That is the simplest option. The next simplest option is to use the Hollow Knight name and the stats for the warforged. Finally, you could do the work to stat up the Hollow Knights using the living construct type. I personally would use the second option, but you might choose something different based on the flavor of your game. Until next time, good luck and good gaming.