This answer is super cheaty, because it always produces the same amount of input, which is equal to \$ \infty \$.
bP&A@?>=<;:9876543210/.-,+*)('&%$T"!~}|;]yxwvutslUSRQ.yx+i)J9edFb4`_^]\yxwRQ)(TSRQ]m!G0KJIyxFvDa%_@?"=<5:98765.-2+*/.-,+*)('&%$#"!~}|utyrqvutsrqjonmPkjihgfedc\DDYAA\>>Y;;V886L5322G//D,,G))>&&A##!7~5:{y7xvuu,10/.-,+*)('&%$#"yb}|{zyxwvutmVqSohmOOjihafeHcEa`YAA\[ZYRW:U7SLKP3NMLK-I,GFED&%%@?>=6;|9y70/4u210/o-n+k)"!gg$#"!x}`{zyxZvYtsrqSoRmlkjLhKfedcEaD_^]\>Z=XWVU7S6QPON0LKDI,GFEDCBA#?"=};438y6543s1r/o-&%*k('&%e#d!~}|^z]xwvuWsVqponPlOjihgIeHcba`B^A\[ZY;W:UTSR4PI2MLKJ,,AFE(&B;:?"~<}{zz165v3s+*/pn,mk)jh&ge#db~a_{^\xwvoXsrqpRnmfkjMKg`_GG\aDB^A?[><X;9U86R53ONM0KJC,+FEDC&A@?!!6||3876w4-tr*/.-&+*)('&%$e"!~}|utyxwvutWlkponmlOjchg`edGba`_XW\?ZYRQVOT7RQPINML/JIHAFEDC&A@?>!<;{98yw5.-ss*/pn,+lj(!~ff{"ca}`^z][wZXtWUqTRnQOkNLhgfIdcFaZ_^A\[Z<XW:U8SRQPOHML/JIHG*ED=%%:?>=~;:{876w43210/(-,+*)('h%$d"ca}|_z\rqYYnsVTpoRPledLLafIGcbE`BXW??TY<:V97S64P31M0.J-+G*(DCB%@?"=<;|98765.3210p.-n+$)i'h%${"!~}|{zyxwvuXVlkpSQmlOjLbafIGcbE`BXW??TY<:V97S64P31M0.J-+G*(D'%A@?"=<}:98y6543,1r/.o,+*)j'&%eez!~a|^tsx[YutWUqjinQOkjMhJ`_dGEaDB^A?[><X;9U86R53O20LKJ-HG*ED'BA@?>7~;:{y7x5.3210q.-n+*)jh&%$#"c~}`{z]rwvutWrkpohmPkjihafI^cba`_^A\[>YXW:UTS5QP3NM0KJ-HGF?D'BA:?>=~;:z8765v32s0/.-nl$#(ig%fd"ca}|_]yrqvYWsVTpSQmPNjMKgJHdGEa`_B]\?ZY<WVUTMR5PO20LK.IHA))>CB%#?87}}49zx6wu3tr0qo-nl*ki'hf$ec!~}`{^yxwvotsrUponQlkMihKIe^]EEZ_B@\?=Y<:V97S64P31M0.J-+GFE(C&A@?8=<;:{876w43s10qo-&%kk"'hf$ec!b`|_]y\ZvYWsVTpSQmlkNiLgf_dcba`C^]\?ZY;WV97SLK33HM0.J-+G*(D'%A$">!};|z8yw543t1r/(-,+*)(i&%fd"!~}|_t]xwvutslqTonmPkjLhKIeHFbEC_^A?[TSX;9UT7R4JIN1/K.,H+)E(&B%#?"~<}{987x/4ussr)p-,m*)ihh}$#d!awv{^\x[YuXVrUSonQlNdchKIeHFbaD_AWV[><X;988MRQ4O1GFK.,++@ED'B$:9>!};:9zy0wuut1*/p-,mk#"hh}$#"cb}v{^\\[vunWrqTonmOkjMLgf_HcbE`_A]@>ZY<:VONS64P31M0.J-+G*(D'%A$">!}||3876wv321*/p-,mk#"'hf$ec!b`|{^y[qpuXVUUjonQOkdchKIeHFbEC_B@\?=Y<:VUT76QPONG0KJ-HGFED'%A:9!!6;:9zy654321*q.-n+*j(ig%fd"ca}`^]]rwvYtVlkpSQmPNMMbgfIdF\[`_^A@[ZYXWVUNS6443NMLKJIHG@)DC&A@?!=<}|98765432+r/.-,+k#('&%e{dy~}|uzsx[vuXsrqpoRPledLLafedGF[`C^]\?ZY;W:8T7544INM0.JCBG*(''<A@#!=65:{yxx/43tr0)(-nlkk"'&ge#zy~a_^^sxwZXtmlqTRQQfkjMKg`_dcbEZ_B]\?=SRW:8T75Q42N1/KJ-+G@?D'%A$">!};|z87x5u-,1rp.-n+k#"'hfeez!~}`_t]xwvYtsUTTinmPNjcbgJHdGEa`_BW\?ZY<WVUTS64PIH00EJIH+*?(&&;@#!!~5:{87xv.-2sq/.om+$#(ig%$e"bxw|_]y\ZvuXsUkjoRPOOdihKfH^]bEC_^A\>TS;;PUTS65JO2MLK.,BA))>CBA$9>!}}|3z765v32r0/p-m%$)jh&ge#"c~`vuz][ZZotsVqSihmPNMMbgfIdF\[`CA@@UZY<W9ONS6433HML/J,BAF)'&&;@?"=}549zx6wutt+0/.on%l)('h%$d"ca}`^z][wvYtVlkpSQmPNjiLJf_^cFDCCX]\?=YRQV9766KPO20LEDI,*))>CB%#?87<}{9zx6wu3tr0/.o&m*)('&%fA/cQ>_^;]87%54"32pRA-yejih:s_GGFDDC^{i[T<XQ9b8r_5]O20Li-zB*SdQPO%##]nml43V1TvS@cs0/_'JJH#jhg%BTd!xw_{t99J6$tV21SBR@?kjcbtJ%^F"DD21]@[xfw;)9Nqq5Jmm~LKWVyx@E't&%:]][~YkF8hgv.tssOMp:&ml6Fi&D1T"y?,O<^s\7vX#Wr2}|Rzl+j<bK`r$F"4ZCk|\?-=RQ
Try it online!
4Should the program in theory work for any input? Or does it suffice to use a method that only works for the specified range (bounded by $\pm 2^{31}$), not necessarily due to language limitations but method limitations? – Mr. Xcoder – 2019-08-16T13:28:30.157
4@Mr.Xcoder how could you pick a length if you had to work for arbitrary length integers? – Stephen – 2019-08-16T13:34:19.703
@Stephen I guess it would be impossible given that the unicode set is limited in length. But I just wanted to clarify that aspect, maybe I'm missing something. – Mr. Xcoder – 2019-08-16T13:36:47.807
2@Mr.Xcoder You must only prove that it works for that range. This rule is to help languages such as Python, where numbers can be thousands of digits. Without that rule, it'd be much harder for both Python, and Python derivatives (which includes a lot of golfing languages). – maxb – 2019-08-16T13:37:01.223
@Arnauld As Mr. Xcoder says, you must avoid all digits in your output. The approach that you take is up to you. If could be transliteration, substitution, dictionary fetching, or something that I haven't thought of. I wanted to leave it quite open, to leave room for creativity. – maxb – 2019-08-16T13:48:03.060
11If a language doesn't have variable length integers but can support values larger than $2^{31}$, are we allowed to use the restricted range $-2^{31}\le n<2^{31}$? – Arnauld – 2019-08-16T15:20:55.347
Can we take input as a string? – Shaggy – 2019-08-16T17:49:32.873
2@Arnauld the maximum range is 32 bit signed integers, regardless of the limitations of the language. The language can only decrease that range. – maxb – 2019-08-16T22:30:13.757
@Shaggy if your language doesn't separate strings and ints, i guess you could. But input should be an integer. Otherwise it'd be too trivial in some languages (I can think of a 3-byter in mathgolf). – maxb – 2019-08-16T22:32:27.737