Good news and bad news.
The good news is that you are correct, that would be they to go. Always do a full sector by sector copy ("dd" would be the go to standard for this) and mess with the old potentially damaged drive as little as possible!

But if you don't have the space for a full copy you will need to get more storage space first. Sure, you could work with compression, but there is no guarantee that this would be enough and it would just make everything vastly more complicated.

Or in the words I would use at work: We need to buy another drive. This is not worth even trying without it. We are likely just going to burn a lot of time without obtaining a useful result. Also we would run the risk of just damaging the old drive/data more with each attempt to read from it.

So you "could" but I would heavily advise against it.

To further emphasize on how important I think excess storage is here:
In fact I would suggest the following setup:
At least twice as much storage as the size of the drive you want to rescue. With the simple reasoning that you want to make the full copy first and then duo all further work with the full backup and restore the data to yet another location in order not to tamper with the potentially corrupted data any further.

Also you might wanna keep that copy in pristine condition until your rescue is complete as further copies might be worse as the disk/filesystem potentially degrades. Worst case every second the drive is running. And on the fly compression makes the process slower.

Good news and bad news.
The good news is that you are correct, that would be the way to go. Always do a full sector by sector copy ("dd" would be the go to standard for this) and mess with the old potentially damaged drive as little as possible!

But if you don't have the space for a full copy you will need to get more storage space first. Sure, you could work with compression, but there is no guarantee that this would be enough and it would just make everything vastly more complicated.

Or in the words I would use at work: We need to buy another drive. This is not worth even trying without it. We are likely just going to burn a lot of time without obtaining a useful result. Also we would run the risk of just damaging the old drive/data more with each attempt to read from it.

So you "could" but I would heavily advise against it.

To further emphasize on how important I think excess storage is here:
In fact I would suggest the following setup:
At least twice as much storage as the size of the drive you want to rescue. With the simple reasoning that you want to make the full copy first and then duo all further work with the full backup and restore the data to yet another location in order not to tamper with the potentially corrupted data any further.

Also you might wanna keep that copy in pristine condition until your rescue is complete as further copies might be worse as the disk/filesystem potentially degrades. Worst case every second the drive is running. And on the fly compression makes the process slower.

Good news and bad news.
The good news is that you are correct, that would be they to go. Always do a full sector by sector copy ("dd" would be the go to standard for this) and mess with the old potentially damaged drive as little as possible!

But if you don't have the space for a full copy you will need to get more storage space first. Sure, you could work with compression, but there is no guarantee that this would be enough and it would just make everything vastly more complicated.

Or in the words I would use at work: We need to buy another drive. This is not worth even trying without it. We are likely just going to burn a lot of time without obtaining a useful result. Also we would run the risk of just damaging the old drive/data more with each attempt to read from it.

So you "could" but I would heavily advise against it.

Good news and bad news.
The good news is that you are correct, that would be they to go. Always do a full sector by sector copy ("dd" would be the go to standard for this) and mess with the old potentially damaged drive as little as possible!

But if you don't have the space for a full copy you will need to get more storage space first. Sure, you could work with compression, but there is no guarantee that this would be enough and it would just make everything vastly more complicated.

Or in the words I would use at work: We need to buy another drive. This is not worth even trying without it. We are likely just going to burn a lot of time without obtaining a useful result. Also we would run the risk of just damaging the old drive/data more with each attempt to read from it.

So you "could" but I would heavily advise against it.

To further emphasize on how important I think excess storage is here:
In fact I would suggest the following setup:
At least twice as much storage as the size of the drive you want to rescue. With the simple reasoning that you want to make the full copy first and then duo all further work with the full backup and restore the data to yet another location in order not to tamper with the potentially corrupted data any further.

Also you might wanna keep that copy in pristine condition until your rescue is complete as further copies might be worse as the disk/filesystem potentially degrades. Worst case every second the drive is running. And on the fly compression makes the process slower.