Hi pink-beauty,
at first, I prefer another classification: voltage controlled voltage feedback (instead of voltage series or - as some other authors define - series-series). That means, the feedback signal is applied as a voltage and is derived from the output voltage. As a typical illustrative example can the opamp serve when used as a noninverting amplifier.
Regarding your question, an emitter resistance always creates a feedback voltage - however, only in common collector (common drain) configuration this voltage is derived from the output voltage. For common emitter (source) and common base (gate) this feedback signal (voltage) is derived from the output current (since the output node is the collector/drain node).
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But, of course, other feedback modes are possible.
For example, in the common emitter configuration you can apply voltage controlled current feedback (feedback path between collector and base). At the base node the input current is superimposed with the feedback current.