You are likely to find it within the thermoplastic elastomers (TPEs). It is a family of six soft materials/material groups: TPE-S, TPE-V, TPE-O, TPE-U, TPE-E, TPE-A. Their advantage is their ability to return to their original shape after being stretched or elongated.
You might have heard of TPR, Thermoplastic Rubber. This is just another name for TPE.
The softness or hardness of TPE’s is measured and indicated on the Shore durometer scale. Some of them are available as a very soft gel and some grades can hardly be described as rubbery or even soft. Typical values are within the Shore A scale between 20 ShA and 90 ShA. This picture presents well the difference between the durometer scales OO, A and D.
TPE’s are commonly used in 2K-molding. Adhesion to the other material is then an important factor when selecting the right TPE grade. Designing 2K components requires a good understanding of the possibilities and the restrictions of the tooling, and the 2K injection-molding process. If unsure, please feel free to contact me.
There are also some thermoplastics outside the TPE family, that can be considered soft or rubbery, like LD-PE, EVA and soft PVC. They are introduced under the commodity path.
Silicone is a particularly heat-resistant option. It is not a thermoplastic and the manufacturing process of silicone products differs from injection molding.