This temporary weakness / paralysis can occur either during or after the laying of an egg and is thought to be caused by the egg pressing on the sciatic nerve.
The hen will have weak or useless eggs and will therefore be unable to walk or to fly and will probably be pulling itself along with its wings. The other pigeons seeing a fellow pigeon that behaves as if it is ill will follow their natural instincts to protect the flock and will attack and peck at the affected hen's head. That will cause her to seek shelter and she risks becoming trapped in small places.
If you see a pigeon that has trouble standing and walking, or is pulling itself along by its wings, it needs to be taken somewhere quiet and warm to rest. If it is likely to be a laying henm then calcium supplements formulated specially for birds, such as Calcivet, Calcivite, Zolcal D or Gen Liquid Calcium, given according to the manufacture's instructions can help strengthen the muscles. They usually recover in a couple of days but they need to be monitored just in case there is an egg that is stuck.
These are most likely to be malformed eggs cause by oviduct problems or oviduct infection. A course of antibiotics should help.
Kesium is the best option but any other amoxycillin clavunate combination such as Synulox or Noroclav will help.
Healthy pigeon eggs are smooth to the touch and this allows their unhindered passage through the oviduct. Sometimes, when there is an infection of the oviduct or a hen is elderly, the eggs can become rough and gritty, which increases the possibility of them becoming egg bound.
Hens that lay rough shelled eggs should be treated with broad spectrum antibiotics for 10 to 14 days, then given calcium supplements according to the manufacturers instructions.
Sometimes a hen will lay an egg that only has a membrane round it or that has a very thin, fragile shell.
This is usually caused by a calcium deficiency and hens showing this problem should have calcium supplements that have been specifically formulated for pigeons, such as Calcivet, Calcivite, Zolcal D and Gem Liquid Calcium, given according to the manufacturer's instructions.
This can be a serious problem that needs veterinary help but as a vet is not always immediately available this advice is designed to help the bird until a vet can be consulted if the egg does not come through naturally.
Egg binding occurs when a hen cannot pass an egg because it is retained in the oviduct.
The symptoms are not necessarily dramatic, the hen looks tired, unable or unwilling to fly, feathers fluffed, not interested in food . Sometimes the vent can be seen to be clenching and unclenching, the pigeon pants and passes liquid faeces.
I know of one case where the symptoms were so dramatic that the bird appeared to be having fits and was assumed to be suffering from poisonig.
Often, the bird's weakness may go unnoticed by humans but will attract the attention of other pigeons that will attack the suffering hen.
If egg binding is suspected immediately place the bird in a cool dark place with supplemental heat from a warm hot water bottle or a Snugglesafe pad. Calcium supplements help strengthen the muscles and can be given according the the manufacturer's instructions.
Sometimes inserting oil into the cloaca with a soft rubber tube can help lubricate the egg. It can also help to give the pigeon a few drops of Liquid Paraffin (I believe this is called mineral oil in the US) orally as this does not get absorbed in the digestive tract and will eventually lubricate the cloaca. But should the problems continue with no egg being produced veterinary advice should be sought.