My strawberry plants have some kind of coating on their stems. It looks like dirt, but I've removed it several times and it keeps coming back. It also follows the stem. It doesn't seem to harm the plant, but it sometimes covers stem ends. This is what it looks like:
Patrick B's question is well placed, because this deposit has the look of ant activity, that is, ant nest building, where you're likely to see little piles of fine soil from their excavations. In this case, they may well be building a nest beneath our around this particular plant, underground. It won't kill your plant, unless their activities disrupt the soil too much round the roots. They don't generally eat strawberries in particular, just in case you were wondering, but if possible, it might be worth lifting the plant to see what's going on (preferably wearing gloves) and relocating it elsewhere if you discover a nest.