There are two types of zones when placing shapes in Orchard - Layout Zones (defined in the Layout.cshtml) and Local Zones (Content item local zones such as Header, Meta, Content, Footer defined by Content.cshtml). The local zones are all rendered within the main Layout's 'Content' zone. The following placement would push your shape to the Footer local zone:
<Match DisplayType="Detail">
<Place Parts_SubscribersForm="Footer:1"/>
</Match>
That is why your form did not seem to move into the footer as you expected. It was in the local Footer zone, but still rendered within the layout's Content zone. Instead you can move your shape to e.g. the Footer Layout Zone by placing a forward slash:
<Match DisplayType="Detail">
<Place Parts_SubscribersForm="/Footer:1"/>
</Match>