Xerochrysum bracteatum
strawflower
The petals are papery and dry to the touch even on a fresh stem, which is why the older name for it is everlasting. It means remembrance that does not require any upkeep.
Native toAcross much of Australia
In seasonYear-round
Vase lifeDries and keeps indefinitely
Pairs withGypsophila · Eucalyptus · Statice
Elsewhere
Sold in Victorian Britain as an everlasting flower for exactly this reason, and dried for winter arrangements long before it was a cut flower.