Perl 5, 87 bytes

Based on the standard quine and my answer to this question:

$_=q{$_="\$_=q{$_};eval";$;='$';@_=/(?<=\Q$;\E).?/g,$;=$_[rand@_]while$;x print$;};eval

As with the faux source code answer, this sometimes produces valid Perl, but very infrequently (<2%):

$_='$;=q[$;\E).?/g,$;\E).?<=$;@_=/g,$';eval
$;=q[rileval"\Q$';eval"\E).?<=q[rale$_]whind@_];eval
$_=q[rand@_=\E).?<=$;=$;$';];evaleval
$_=';evale$_=q[$;\Q$;evant$_]whind@_=\E).?/g,$_[$;@_];];=/(?<=/g,$;];=$';eval
$_='$;\Q$;$;@_=/g,$;=\Q$_=$_=$_[rind@_=\$;@_=$_];$_];=\Q$;evand@_=\Q$_=$';eval
$_=q[rand@_=q[rind@_='$';\Q$_];=$';];evaleval
$_=";];\Q$;=/g,$;=$;\Q$;evant$;\Q$';];x pril";$_=q[$;];eval
$;='$_];$;\Q$_=q[ralevant$_=q[$_=\$;\$;$;=q[$_[$;evale$;@_=q[rand@_];=q[$_=';evaleval

Try it online!

Perl 5, 81 bytes

Based on the standard quine and my answer to this question:

$_=q{@$=a^E;@$="\$_=q{$_};eval"=~/(?<=\Q$@\E).?/g,print$@while$@=$$[rand@$]};eval

Try it online!

As with the faux source code answer, this sometimes produces valid Perl, but very infrequently (<2%):

$$$_=al
$_=a^E;eval
$_=al
$$=q{$$]};eval
$@=a^E;@whil
$_=q{@\E;e$]};evaleva^E;eval
$$=q{@\$_=a^E;evant$@$="=$$]};evaleval
$_=q{@whind@$_=$]};eval
$_=q{@\$@=~/(?<=\$[rilevale$=ant$[rint$_};evaleval
$_=aleval
$_=q{@$_};@whil
$$=q{@$=q{@$=\E;evand@whint$_};eva^E).?<=$=~/g,prand@$_=al"\E;e$@\E).?/g,prant$_};evaleval
$_=\$_=~/g,prind@=q{$]};@$@\Q$$$_};e$@$_=q{@$_=~/g,pril
$_=q{$=aleval"\E;evaleva^E;eva^E).?/g,pra^E;eva^E).?/(?/g,print$@$_};eval
$@=q{$_=~/(?<="\$_};eval

Perl, 103 bytes

Based on the standard quine and my answer to this question:

$_=q{$_="\$_=q{$_};eval";@s='$';{push@s,(@n=/(?<=\Q$s[-1]\E)(.|$)/g)[rand@n];$s[-1]&&redo}print@s};eval

Example Output

$_=q{$_=q{$_=";@sh@s=";eval
$_="\$_=q{$_='$_=q{$_}pus=\$_=";@n=";@ndo};{pus=';edo};@n]\Q$_};{$_};@s=q{$_=';@s[rand@s=/g)(@s,(@s,(@sh@s[-1];@ndo};ed@s[-1]\E)(.|$_}prevan]&ral";evan];{$_}pus='$_};ed@sh@sh@s[-1]\$_='$_};evando};eval
$_=q{$_=";ed@s[-1];evand@s="\Q$_=";@s[-1]\Q$_=q{$_=";@nd@sh@sh@s='$_=q{$_=q{$_='$_="\Q$_='$_};{pus=\$_=q{$_}pral
$_=";evando};@nd@sh@s,(@n]\$_=";@s,(@s[-1];{$_=q{$_}pral
$_=";eval
$_='$_=q{$_="\$_="\Q$_=";ed@sh@s=\E)(.|$_=q{$_=q{$_=q{$_=q{$_}pus=/(?<=q{$_};eval
$_=";ed@sh@s[-1]\Q$_=';edo};{$_=q{$_=";@nt@s,(@n]&&&&&&&ral";@nd@s,(@s[-1]\$_}pus=\E)(.|$_=';@nt@s[ral

Similarly to the other question, some results generate valid Perl:

$_=q{$_};{$_};eval";@sh@s[-1]\$_='$_};evan]\Q$_}preval";eval
$_=q{$_};{$_=q{$_=';@nd@s=q{$_};@s[-1]\E)(@s[-1]\E)(@n=';edo};{$_}predo};eval
$_=q{$_=q{$_};edo};@n=q{$_=q{$_};@s[rin='$_=q{$_}pus=/g)(.|$_=q{$_};edo};eval
$_=q{$_};eval
$_=q{$_=";@ndo};{$_}preval

but the chances are slightly lower, at ~2%.

Perl 5, 87 bytes

Based on the standard quine and my answer to this question:

$_=q{$_="\$_=q{$_};eval";$;='$';@_=/(?<=\Q$;\E).?/g,$;=$_[rand@_]while$;x print$;};eval

As with the faux source code answer, this sometimes produces valid Perl, but very infrequently (<2%):

$_='$;=q[$;\E).?/g,$;\E).?<=$;@_=/g,$';eval
$;=q[rileval"\Q$';eval"\E).?<=q[rale$_]whind@_];eval
$_=q[rand@_=\E).?<=$;=$;$';];evaleval
$_=';evale$_=q[$;\Q$;evant$_]whind@_=\E).?/g,$_[$;@_];];=/(?<=/g,$;];=$';eval
$_='$;\Q$;$;@_=/g,$;=\Q$_=$_=$_[rind@_=\$;@_=$_];$_];=\Q$;evand@_=\Q$_=$';eval
$_=q[rand@_=q[rind@_='$';\Q$_];=$';];evaleval
$_=";];\Q$;=/g,$;=$;\Q$;evant$;\Q$';];x pril";$_=q[$;];eval
$;='$_];$;\Q$_=q[ralevant$_=q[$_=\$;\$;$;=q[$_[$;evale$;@_=q[rand@_];=q[$_=';evaleval

Try it online!

Perl, 103 bytes

Based on the standard quine and my answer to this question:

$_=q{$_="\$_=q{$_};eval";@s='$';{push@s,(@n=/(?<=\Q$s[-1]\E)(.|$)/g)[rand@n];$s[-1]&&redo}print@s};eval

Example Output

$_=q{$_=q{$_=";@sh@s=";eval
$_="\$_=q{$_='$_=q{$_}pus=\$_=";@n=";@ndo};{pus=';edo};@n]\Q$_};{$_};@s=q{$_=';@s[rand@s=/g)(@s,(@s,(@sh@s[-1];@ndo};ed@s[-1]\E)(.|$_}prevan]&ral";evan];{$_}pus='$_};ed@sh@sh@s[-1]\$_='$_};evando};eval
$_=q{$_=";ed@s[-1];evand@s="\Q$_=";@s[-1]\Q$_=q{$_=";@nd@sh@sh@s='$_=q{$_=q{$_='$_="\Q$_='$_};{pus=\$_=q{$_}pral
$_=";evando};@nd@sh@s,(@n]\$_=";@s,(@s[-1];{$_=q{$_}pral
$_=";eval
$_='$_=q{$_="\$_="\Q$_=";ed@sh@s=\E)(.|$_=q{$_=q{$_=q{$_=q{$_}pus=/(?<=q{$_};eval
$_=";ed@sh@s[-1]\Q$_=';edo};{$_=q{$_=";@nt@s,(@n]&&&&&&&ral";@nd@s,(@s[-1]\$_}pus=\E)(.|$_=';@nt@s[ral

Similarly to the other question, some results generate valid Perl:

$_=q{$_};{$_};eval";@sh@s[-1]\$_='$_};evan]\Q$_}preval";eval
$_=q{$_};{$_=q{$_=';@nd@s=q{$_};@s[-1]\E)(@s[-1]\E)(@n=';edo};{$_}predo};eval
$_=q{$_=q{$_};edo};@n=q{$_=q{$_};@s[rin='$_=q{$_}pus=/g)(.|$_=q{$_};edo};eval
$_=q{$_};eval
$_=q{$_=";@ndo};{$_}preval

but the chances are slightly lower, at ~2%.

Perl, 103 bytes

Based on the standard quine and my answer to this question:

$_=q{$_="\$_=q{$_};eval";@s='$';{push@s,(@n=/(?<=\Q$s[-1]\E)(.|$)/g)[rand@n];$s[-1]&&redo}print@s};eval

Example Output

$_=q{$_=q{$_=";@sh@s=";eval
$_="\$_=q{$_='$_=q{$_}pus=\$_=";@n=";@ndo};{pus=';edo};@n]\Q$_};{$_};@s=q{$_=';@s[rand@s=/g)(@s,(@s,(@sh@s[-1];@ndo};ed@s[-1]\E)(.|$_}prevan]&ral";evan];{$_}pus='$_};ed@sh@sh@s[-1]\$_='$_};evando};eval
$_=q{$_=";ed@s[-1];evand@s="\Q$_=";@s[-1]\Q$_=q{$_=";@nd@sh@sh@s='$_=q{$_=q{$_='$_="\Q$_='$_};{pus=\$_=q{$_}pral
$_=";evando};@nd@sh@s,(@n]\$_=";@s,(@s[-1];{$_=q{$_}pral
$_=";eval
$_='$_=q{$_="\$_="\Q$_=";ed@sh@s=\E)(.|$_=q{$_=q{$_=q{$_=q{$_}pus=/(?<=q{$_};eval
$_=";ed@sh@s[-1]\Q$_=';edo};{$_=q{$_=";@nt@s,(@n]&&&&&&&ral";@nd@s,(@s[-1]\$_}pus=\E)(.|$_=';@nt@s[ral

Similarly to the other question, some results generate valid Perl:

$_=q{$_};{$_};eval";@sh@s[-1]\$_='$_};evan]\Q$_}preval";eval
$_=q{$_};{$_=q{$_=';@nd@s=q{$_};@s[-1]\E)(@s[-1]\E)(@n=';edo};{$_}predo};eval
$_=q{$_=q{$_};edo};@n=q{$_=q{$_};@s[rin='$_=q{$_}pus=/g)(.|$_=q{$_};edo};eval
$_=q{$_};eval
$_=q{$_=";@ndo};{$_}preval

but the chances are slightly lower, at ~2%.