Radiation softened quine

Question

It's simple: Make a proper quine where if you remove any character, it's still a quine.

The difference between this and a radiation hardened quine is that if your program is AB, in a radiation hardened quine A would output AB, but here, A would output A.

Code golf, all standard rules, standard loopholes apply, no cheating.

Answer 1

Lenguage, 4.54×10⁷⁶¹ bytes

It has this number of null characters:

453997365974271498471447945720930600149036031871190716908688344432973027776681259141680552038829875159204621651993092104775733418288411812715164994750890484868305218411129600012389568016974351721147925344946382782884546247102886167837964612372737300786173159265347137401863281368021545169383664534228503236761742285358985343373496184959796553930661837467682191561275123057706776367104142995491262443697167483190110516522677811931124842961701222425076750211774387637740969301686178545299089832300154448308384461700726890067468872402133010536518468336342175124002115991866466700174974019423711837589532744970385003356612639263433822126850314801275940879069069974437167102618471264140597777702065896715558989678487253830854848740247786166790545462769498303055791292

Seeing how the criterion in this challenge conflicts with the definition of a "proper quine", seriously, I think an Unary variant is going to win.

Expanded Brainfuck code:

>>+++>++++++++>+++>+++>+>+>+>+>+>+>+>+++>+>+>+>+>+>+>+>+>+++>+>+>+>+>+>+>+>+>++++++++>++++>++++++++>++++>+++++++>++>+++>+>+++>++>+++>+++>+>+>+>+>+>+>+>+>++++>++++>+++++++>+>++++>++++++++>++>+++++++>+++>++++++++>++>+++++++>+++>++++++++>++>+++++++>+++>++++++++>++>+++++++>+++>+++++>++++++++>++++>+++++++>+++++++>+>+>+++>+>+>+>++++++++>+++>+++++++>+>+++>+>+++>+>+++>+>++++++++>++++>++++++++>++++>++++++++>++++>++++>+>+++>+++>++>+++++++>+++++++>+>+>+>++++++++>+++>+>++++++++>++++>+>+++>++>+++++++>++>+++++++>++++>++++>++++++++>+++>++++++++>+++>+++>+>++++>++++>++>+++++++>+++>+++>++++++++>++++>+>+++>++>+++++++>++++>++++>+++++++>+++>+++>+++>+++>++++++++>++++>++++>+>+++>+>+++>++>+++++++>+++++++
[
    [->+>+<<]
    >>>>[<<[->+<]>>[-<<+>>]>]
    <<[-[->+<]+>]+++
    [[->>+<<]<]<
]
+>+>+>+
[>]+++>++
[
    [<].
    >[-]>[-]>[-]>[-]
    <+[<<++++++++>>->+>-[<]<]
    ++++++++>++++++++>+++++++>>
]
.

If one character is removed from the Lenguage program, the last character becomes a <, which causes the program to print exactly one less character.

Answer 2

><> (Fish), 145 107 bytes

This answer uses ><>'s jumping instruction to fix the problem.

!<0078*+00~..>0[!."r43a*+8a+&{ee+00&1-:&(?.~~ol?!;4b*0.0f<>0['r3d*159*+&}7a*00&1-:&(?.~~ol?!;68a*+0.0+*a58 

This quine actually contains two different quine generators. It starts with some jumping logic and by default uses the left quine. If a character is removed from the jumping logic or from the left quine, the program jumps to the right quine.

You can try it here

Explanation

The code can be dissected into a few parts:

A: !<0078*+00~..>0[!. 
B:              >0[!."r43a*+8a+&{ee+00&1-:&(?.~~ol?!;4b*0.
C:                                                    .0f<
D:                                                        >0['r3d*159*+&}7a*00&1-:&(?.~~ol?!;68a*+0.
E:                                                                                                 .0+*a58 

Explanation of the different parts:

• A: Jumps to the right of C. If any character is deleted from from A, this jumps to the left of D or the right of E, triggering the second quine. If any character is deleted from B or C, the code is shifted 1 character to the left, causing this to jump to the left of D.
• C: This code jumps to the left of B.
• B: Quine #1
• D: Quine #2
• E: Jumps to the left of D

Explanation of the quine (with #1 as example):

Once the instruction pointer reaches either of the quines, you're certain that that quine is completely intact.

>0[!.                                       //Fix the instruction pointer's direction and empty the stack (The '!.' is a leftover from codepart A)
     "r43a*+                                //Start reading all of the code and add the '"' character to the stack
            8a+&                            //Because the quine started reading at the 19th character instead of the first, the stack has to move 18 characters. 
                                            //This part saves the number 18 to the register.
                {ee+00&1-:&(?.              //Move the stack one to the left, decrease the stack by 1. If the stack is not empty yet, jump back to the start of this section.
                              ~~              //Clean the temporary variables from the stack. It should now contain the whole quine.
                                ol?!;4b*0.  //Print the first character from the stack. As long as the stack isn't empty, jump back to the start of this section.