This is the general rule: Whatever is permitted during a part of the Sabbath remains permitted throughout the Sabbath and whatever is forbidden during a part of the Sabbath remains forbidden throughout the Sabbath, the only exception being the case of the man who renounced his share.
So what does the first part mean?
‘Whatever is permitted during a part of the Sabbath remains permitted throughout the Sabbath’, as is, for instance, the case of an eruv that was prepared for the purpose of carrying objects through a certain door and that door was closed up, or one that was prepared for the purpose of carrying objects through a certain window and that window was closed up.
That is, if an eruv is prepared say between two courtyards and the connection between those two courtyards collapses on Shabbat, the eruv remains intact through the Shabbat. For example, one could throw an object from one courtyard to another or pass things through a hole – both only permitted within an intact eruv.
‘Whatever is forbidden during a part of the Sabbath remains forbidden throughout the Sabbath’, as, for instance, in the case of two houses, that were respectively situated on the two sides of a public domain which gentiles surrounded with a wall during the Sabbath. What does the expression ‘This is the general rule’, include? It includes the case of a gentile who died on the Sabbath.
Perhaps, upon his death during the Sabbath day, the share of the courtyard which was held by a gentile whose possession of it precluded the use by Jews who also shared (all owners of the courtyard have to agree and participate in the eruv or none can) would be opened up. No, because it was forbidden at the beginning of the Sabbath, it remains so throughout.
Now here it was stated: ‘The only exception being the case of the man who renounced his share’, from which it follows, does it not, that only he may do so but not his heir? — Read, ‘The only exception being the law of renunciation’.
Does the exception mentioned mean that if the (Jewish) owner of a share died on the Sabbath and he had neglected to dedicate his share to the eruv, his son who inherits renounce that share of the courtyard during the Sabbath?
Not if the final phrase is read “. . .the case of the man who renounced his share” – his share, not his father’s! But if it is read “. . .the law of renunciation” then it would be allowed.