All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Yes, it is permissible for a person whose hand is broken and plastered to wipe over the plaster when he wants to purify himself for the prayer as long as he needs the plaster, whether that purification is from minor impurity or major impurity.
It is reported in a Hadeeth that the Prophet said about a man who suffered a severe head injury: "He has to wipe over his head and wash all his body." [Abu Daawood]
Therefore, a person who had prayed in this condition does not have to repeat the prayers that he had performed while wiping over the plaster. However, if a person has plaster on any part of his body and performed prayers without wiping over the plaster when making Ghusl (i.e. ritual bath), ablution or Tayammum (dry ablution) [if he is allowed to perform the latter], then his prayer is invalid. The Prophet said: "The prayer is not accepted without purification." [Muslim]
Therefore, in such a case, such a person has to make up for the prayers that he had performed in that condition while he was able to use water or soil.
However, if he was unable to use water or soil neither directly or for wiping, and neither by himself nor with the help of somebody else, then the ruling that applies to him is that he cannot perform ablution or Tayammum (dry ablution), and so, he should pray as he is.
Nonetheless, the scholars differed about this issue.
Allaah Knows best.