The only way I know of to prevent this “stretching” (actually the hair is likely just straightening out some, losing some of its curvature) is by applying Weights > 0 to the hair strand keys, in Particle Edit mode. This is much like Weight Painting a mesh, but the purpose is to preserve the styled shape of the strands.
A lot depends on the initial styling & Hair Dynamics parameters, but in general, weights above 0.30 will start to noticeably affect the “stretching” you speak of. But this also affects how pronounced the Hair Dynamics are when baked. So you’ll have to do a trade-off of sorts, between preserving the initial styling and getting the hair to move well. At weight 1.0 (bright red in the viewport) the strands are perfectly stiff but do not show any response to Hair Dynamics. At weight 0 (dark blue) the strands respond fully to Hair Dynamics and frequently lose much of their styling as a result. By painting rows or other groupings of strand keys at different weights you control the style distortion and response to Hair Dynamics.
For some styles, it may be necessary to compensate in the styling for the effects of Hair Dynamics, for example, if the strands lengthen & lose their curve, then shorten the initial style & deepen its curves. It takes some testing to get the best effect but it does provide a workaround.