Yes. That happens when the tree is not getting enough energy from its fronds. Many times people remove dead fronds from a palm tree not knowing that they are still feeding the healthy green fronds and immature new fronds.
Palm tree's tropical heritage means they never developed good energy storage capacity since there is usually sun and nutrients all year round. So if stress or environmental factors hit it, it has no choice but to use cannabalize the trunk for energy for photosynthesis.