What is the fix to correct this. The ceiling was opened up and branch circuit wires were cut. Can a junction box be installed in the attic to properly secure the added wire back to the panel?
As long as the J-box is not “hidden” and remains available for access.
these are also available.
http://www.te.com/catalog/bin/TE.Connect?C=11621&F=0&M=CINF&GIID=0&LG=1&I=13&RQS=C~11621
IIRC there are certain conditions before those Amp connectors can be used.
See this link, pg 5 and 6. Note, there is an error on Pg 5. The word finished should be fished.
http://www.ampnetconnect.com/documents/NM_Connector_Presentation_Rev4_Web_%5B090123%5D.pdf
[FONT=Arial][size=6][FONT=Arial][size=6]• [/size][/FONT][/size][/FONT]***[FONT=Arial][size=6][FONT=Arial][size=6]2005 and 2008 National Electrical Code:
*[/size][/FONT][/size][/FONT]**334.40 Boxes and Fittings
(B) Devices of Insulating Material. Switch, outlet, and tap devices
of insulating material shall be permitted to be used without boxes in
exposed cable wiring and for rewiring in existing buildings where the
cable is concealed and fished. Openings in such devices shall form a
close fit around the outer covering of the cable and the device shall
fully enclose the part of the cable from which any part of the coverings
has been removed. Where connections to conductors are by binding
screw terminals, there shall be available as many terminals as
conductors.
According to Mike’s Link it meets;\
Meets requirements of National Electrical Code, Articles 545, 550, 551
I don’t know what those Articles are. You might Jim. 
So everywhere except new work that permits NM?
**ARTICLE 545
Manufactured Buildings
**[FONT=Times-Bold]ARTICLE 550
Mobile Homes, Manufactured Homes,
and Mobile Home Parks
**
**ARTICLE 551
Recreational Vehicles and Recreational
Vehicle Parks
I believe you meant New Work, not New York.
**
**[/FONT]
You’re right , Edited.
You didn’t answer my question.
Can you use it to solve the OP problem or not?
Jim, does that mean pretty much Manufactured Housing as I see this?
That was where these started Marcel.
To be honest Mike, I am not sure, but would lean towards No. Perhaps Robert will weigh in.
FYI from an electricians MB
[/size][/FONT]
I have known of those connections for awhile now, but never come across them yet.
It would be fitting for Manufactured Homes. That is usually where one finds unusuall building practices. :)
I have not seen them either but if it is allowed to be concealed as it appears, you wouldn’t 
I researched these a few years ago.
Concealed huh!
My issue would be that the cable in this case would neither be fished or concealed. They would be concealed after the fact, but I take that section to mean the cables are already installed and you are tapping from them.
I am envisioning something like a cable is running between two boxes and you wish to install another box in between the two. This product could be used to tap into the cable run with a short cable and the box installed for the receptacle.
From what I read electricians don’t like them but I see no restrictions on their use.
They are however insulated and secured to each other.
The manufacture states they are permissible so as usual the local AHJ would have to make the call and I don’t see what he would use to deny their use.
Handy in certain situations like moving an existing circuit around a new door opening.