user21539: Is it possible to include a blank input in a transaction?
For example, a blank input could be used to guarantee a particular output was included in a transaction, using SIGHASH_SINGLE | ANYONECANPAY in combination with SIGHASH_NONE. 
Of course you would still need to include miner fees within another input. 
Correct me if I am wrong, but although spending 0-output utxos is legal, it is fairly difficult to generate 0-output utxos, as Bitcoin Core does not support generating these transactions beneath the dust limit.
Likewise, OP_RETURN provides 0-value-output utxos, but they could not be spent as part of a sighash_single, since they are unspendable.

user7272: 
For example, a blank input could be used to guarantee a particular output was included in a transaction, using SIGHASH_SINGLE | ANYONECANPAY in combination with SIGHASH_NONE.

You cannot use SIGHASH_SINGLE | ANYONECANPAY in combination with SIGHASH_NONE. You cannot have two or more of SINGLE, ALL, NONE on a single input, they can only be combined with ANYONECANPAY.
Moreover, if you are able to create a zero value (or even dust output), that single output alone will be enough to enforce the rule "If you use this output, you must send X BTC to this address". However, if you have a zero value or dust output, no one is really incentivized to include it - after all, you aren't contributing any significant value to the tx. In fact, you are raising the fee due to the extra input/output size. People will just drop your input and output and build a tx without it.

21539: <p>Is it possible to include a blank input in a transaction?</p>

<p>For example, a blank input could be used to guarantee a particular <code>output</code> was included in a transaction, using <code>SIGHASH_SINGLE | ANYONECANPAY</code> in combination with <code>SIGHASH_NONE</code>. </p>

<p>Of course you would still need to include miner fees within another input. </p>

<p>Correct me if I am wrong, but although spending 0-output utxos is legal, it is fairly difficult to generate 0-output utxos, as Bitcoin Core does not support generating these transactions beneath the dust limit.</p>

<p>Likewise, OP_RETURN provides 0-value-output utxos, but they could not be spent as part of a <code>sighash_single</code>, since they are unspendable.</p>
 7272: <blockquote>
  <p>For example, a blank input could be used to guarantee a particular output was included in a transaction, using SIGHASH_SINGLE | ANYONECANPAY in combination with SIGHASH_NONE.</p>
</blockquote>

<p>You cannot use <code>SIGHASH_SINGLE | ANYONECANPAY</code> in combination with <code>SIGHASH_NONE</code>. You cannot have two or more of <code>SINGLE</code>, <code>ALL</code>, <code>NONE</code> on a single input, they can only be combined with <code>ANYONECANPAY</code>.</p>

<p>Moreover, if you are able to create a zero value (or even dust output), that single output alone will be enough to enforce the rule "If you use this output, you must send X BTC to this address". However, if you have a zero value or dust output, no one is really incentivized to include it - after all, you aren't contributing any significant value to the tx. In fact, you are raising the fee due to the extra input/output size. People will just drop your input and output and build a tx without it.</p>
