I can't seem to get the dependent dropdown to clear its value, but this does show the dependent search having a cleared value from the dependent dropdown until a new value is selected:
<form>
<label>States</label>
<search id="states">
<query>| makeresults | eval state="Alabama,Alaska,Arizona,Arkansas,California,Colorado,Connecticut,Delaware,Florida,Georgia,Hawaii,Idaho,Illinois,Indiana,Iowa,Kansas,Kentucky,Louisiana,Maine,Maryland,Massachusetts,Michigan,Minnesota,Mississippi,Missouri,Montana,Nebraska,Nevada,NewHampshire,NewJersey,NewMexico,NewYork,NorthCarolina,NorthDakota,Ohio,Oklahoma,Oregon,Pennsylvania,RhodeIsland,SouthCarolina,SouthDakota,Tennessee,Texas,Utah,Vermont,Virginia,Washington,WestVirginia,Wisconsin,Wyoming" | makemv delim="," state | table state | mvexpand state</query>
</search>
<fieldset submitButton="false">
<input type="dropdown" token="letter" searchWhenChanged="true">
<label>Letter</label>
<fieldForLabel>letter</fieldForLabel>
<fieldForValue>letter</fieldForValue>
<search base="states">
<query>
<![CDATA[rex field=state "^(?<letter>.)" | stats count BY letter]]>
</query>
</search>
<change>
<unset token="state" />
</change>
</input>
<input type="dropdown" token="state" searchWhenChanged="true">
<label>State</label>
<fieldForLabel>state</fieldForLabel>
<fieldForValue>state</fieldForValue>
<search base="states">
<query>
<![CDATA[rex field=state "^(?<letter>.)" | search letter=$letter$]]>
</query>
</search>
</input>
</fieldset>
<row>
<panel>
<title>You picked</title>
<single>
<search base="states">
<query>search state=$state$ | table state</query>
</search>
<option name="drilldown">none</option>
</single>
</panel>
</row>
</form>
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