A soft spring (possibly also known as a "weak" spring in FE parlance) is a term used to define a spring element where the spring stiffness -- or spring rate depending on which side of the pond you lie on -- in units of Force/length is small relative to the body it is attached to (and therefore has little influence of the behaviour of the body it is attached to other than to stop rigid body motion).
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They are sometimes used in contact analysis, where there can be a sudden change from relative stiffness (in one direction) to rigid body movement (in the other direction).
If you need the info for a vibration calculation: a soft spring typically has a low stiffness, leading to natural frequencies of the total system, well below sources of excitation. In such case, the installation is operated under-critical. Typical examples are resiliently mounted engines or installations.
