Two adjectives carry this question, flexible and rigid, and each is a label a clinician attaches to a toe. Read the label literally and you know what it promises and what it leaves out.
The answer sits in the word flexible
Cleveland Clinic says podiatrists group hammertoes into three types based on their severity. It defines the flexible type as one where you can still bend and move the affected toe, but a noticeable curl is starting to form. The definition turns entirely on movement, and rigid is the label set against it.
What the wording tells you
Because the three types are sorted by severity, flexible is a position on a scale, not a verdict on its own. The Royal National Orthopaedic Hospital's patient guide to bunions and lesser toe deformities is a longer document to read before your appointment, so you can see how a hospital words the same distinctions.
What to confirm, and with whom
Ask the foot doctor you see which of the three types your toe falls into, and what they checked to decide. In Itasca that conversation is one a podiatrist or foot and ankle surgeon can have with you in the exam room. Get the answer in the chart, in words, so that later notes and any treatment discussion refer to the same label.
If the toe also rubs against a shoe, the APMA page on corns and calluses deals with that skin problem separately from the toe's shape.
The phrase most readers skip
The Cleveland Clinic definition says a curl is "starting to form." That small clause marks the flexible type as the early one in its wording, so do not read it as a settled description of how your toe will stay.