Pyth, 9 bytes

>1fqz`sTy

Check out the test suite!

Outputs only one possible solution, wrapped in a singleton list as allowed by default (e.g. ([1...10], 10) -> [[1,2,3,4]]; ([], 0) -> [[]]). For unsolvable inputs, it returns [], which is falsey in Pyth.

For a clearer output, without using the singleton-list rule and using 0 rather than [] as a falsy value, it is possible to solve the challenge in 10 bytes.

Explanation

First, the code computes the powerset of the input list (all possible ordered sub-collections thereof). Then, it only keeps those collections whose sum is equal to the input number. It should be noted that the collections are generated from the shortest to the longest, so we focus on the last one. To obtain it:

• The 9-byter takes the last element, but using the equivalent Python code lst[-1:] in place of lst[-1] to avoid errors from being thrown for unsolvable inputs.
• The 10-byter prepends a 0 to the list of filtered sub-collections, then takes the end of that collection (last element). If the inputs aren't solvable, then 0 is naturally used instead.

Pyth, 8 bytes

• 8-byter (Try it!) – Outputs only one possible solution. For unsolvable inputs, it doesn't print anything to STDOUT, which is an empty string, which is technically speaking falsey in Pyth, but writes to STDERR. Thanks to FryAmTheEggman for suggesting this (ignoring STDERR and focusing on the STDOUT output only), thus saving 1 byte.

    efqz`sTy    
  

• 9-byter (Try it!) – Outputs only one possible solution, wrapped in a singleton list as allowed by default (e.g. ([1...10], 10) -> [[1,2,3,4]]; ([], 0) -> [[]]). For unsolvable inputs, it returns [], which is falsey in Pyth.

    >1fqz`sTy
  

• 10-byter (Try it!) – For a clearer output, without using the singleton-list rule and using 0 rather than [] as a falsy value.

    e+0fqz`sTy
  

Explanation

First, the code computes the powerset of the input list (all possible ordered sub-collections thereof). Then, it only keeps those collections whose sum is equal to the input number. It should be noted that the collections are generated from the shortest to the longest, so we focus on the last one. To obtain it:

• The 8-byter simply uses the end built-in, which throws an error, but STDERR can be ignored as per our site rules, the output to STDOUT being an empty string, which is falsy.
• The 9-byter takes the last element, but using the equivalent Python code lst[-1:] in place of lst[-1] to avoid errors from being thrown for unsolvable inputs.
• The 10-byter prepends a 0 to the list of filtered sub-collections, then takes the end of that collection (last element). If the inputs aren't solvable, then 0 is naturally used instead.

Pyth, 9 bytes

>1fqz`sTy

Check out the test suite!

Outputs only one possible solution, wrapped in a singleton list as allowed by default (e.g. ([1...10], 10) -> [[1,2,3,4]]; ([], 0) -> [[]]). For unsolvable inputs, it returns [], which is falsey in Pyth.

For a clearer output, without using the singleton-list rule and using 0 rather than [] as a falsy value, it is possible to solve the challenge in 10 bytes.

Pyth, 9 bytes

>1fqz`sTy

Check out the test suite!

Outputs only one possible solution, wrapped in a singleton list as allowed by default (e.g. ([1...10], 10) -> [[1,2,3,4]]; ([], 0) -> [[]]). For unsolvable inputs, it returns [], which is falsey in Pyth.

For a clearer output, without using the singleton-list rule and using 0 rather than [] as a falsy value, it is possible to solve the challenge in 10 bytes.

Explanation

First, the code computes the powerset of the input list (all possible ordered sub-collections thereof). Then, it only keeps those collections whose sum is equal to the input number. It should be noted that the collections are generated from the shortest to the longest, so we focus on the last one. To obtain it:

• The 9-byter takes the last element, but using the equivalent Python code lst[-1:] in place of lst[-1] to avoid errors from being thrown for unsolvable inputs.
• The 10-byter prepends a 0 to the list of filtered sub-collections, then takes the end of that collection (last element). If the inputs aren't solvable, then 0 is naturally used instead.