At the bottom of Eruvin 65b,  a case is brought where 3 sages of the transition/early Amoraic period, Rabbi Chanina bar Yosef, Rabbi Chiya bar Aba, and Rabbi Assi spent shabbos at an inn owned by a non-Jew.
The owner was not present before shabbos for them to hire his “reshus” from him, and according to the view of Rabbi Yehuda that if the non-Jewish resident/owner is not present over shabbos, he forms no barrier to the eruv, they could have made an eruv before shabbos without him, but even if they did, now that he was back, it was no longer valid, and  they asked each other whether  this שכירת רשות  could be performed on shabbos. (there is some debate amongst the Rishonim as to whether they did indeed make an eruv before shabbos and whether they held like Rabbi Yehuda or not.)
The basis of their uncertainty was whether שכירת רשות  is forbidden on shabbos just like making the actual eruv is, or whether it is permitted like בטול רשות  is according to Beis Hillel (see Mishna on Eruvin 69b and Gemara on it)
It seems to me  that the basis of their uncertainty could be as follows.
On the one hand, it could be a form of transaction which effectively gives them control of the space, and is thus included in the prohibition of מקח וממכר  (commerce) on shabbos, just like the actual ערוב חצירות  process is, and like Beis Shamai also view בטול רשות  ( as explained by the Gemara on Eruvin 71a)
On the other hand, it could be simply a form of סלוקי רשות, (removing one’s own rights to the object) like how Beis Hillel view בטול רשות (see also Eruvin 71a) and thus permitted.
A deeper analysis of the conceptual mechanisms by which the above processes work is needed, particularly regarding how שכירות  can possibly resemble מחילה  and just be considered as סלוקי רשות  when the renter clearly seems to be an active part of the process- it certainly seems from this that we are not dealing with a real rental, but some form of symbolic rental with its own set of laws (see Meiri who makes this point.)
For our purposes, we shall note that Rabbi Chanina bar Yosef was in favor of going ahead with the שכירות, Rabbi Assi was against it, and Rabbi Chiya bar Aba suggested that they follow the lenient view of the “elder” Rabbi Chanina bar Yosef and go ahead.
After the event, they asked Rabbi Yochanan about this, and he praised their actions.
This attracted the surprise of Nehardai, given that Rabbi Yochanan had ruled previously that שוכר כמערב דמי  (the one who performs this שכירות רשות  is subject to the laws of one who makes the eruv,) and going by that, he should have been against their lenient treatment of שכירות רשות  as בטול רשות  that permitted it on shabbos.
The Gemara responds that in keeping with the general rule that most principles of eruvin are said to produce leniencies and not stringencies (see Rashi), Rabbi Yochanan’s application of the law of the מערב  (eruv maker) to the שוכר  (renter) only extends to the leniencies of the מערב  and not its stringencies, such as being valid with less than the value of a פרוטה  and the other leniencies listed on the daf.
This could be because Chazal treated  שכירות רשות  as a form of hybrid mechanism which takes on the leniencies of both עירוב  and בטול רשות  and neither of their unique stringencies- alternatively Rabbi Yochanan could have simply been unsure as to which mechanism it follows and ruled leniently either way.
This seems  to be yet another example of how lenient Chazal were with the requirements of Eruvin, even above their normal leniencies applied to all rabbinic laws. We saw this earlier  regarding the rule of הלכה כדברי המקיל בערוב  in that even a minority lenient opinion might be followed in an unsettled dispute (see posts on Eruvin 46 and 47.)

Usually we are not entitled to be lenient in rabbinic matters in two different ways that create  a paradox or situation of תרתי דסתרי .
For example, one may be lenient and daven Mincha after plag hamincha in accordance with Rabbi Yehuda or choose to be lenient and daven Maariv straight after plag hamincha before nightfall in accordance with the Chachamim (see Brachos 27a,) but one may not follow both leniencies and daven both Mincha and Maariv during the time between plag and nightfall.
One must choose whether to treat that time as night or day but cannot treat it as both on the same day, and certainly does not treat it as a hybrid.
Yet, in our case, we are not forced to choose whether to treat the שכירת רשות  process leniently like מערב  regarding using less than a  שוה פרוטה  or treating the שכירת רשות  process leniently like בטול רשות  and permitting it on shabbos- rather  we are able to treat it leniently like both, despite is seeming logically paradoxical.
This is no small thing, and further analysis is required to assess if the above comparison is indeed accurate, as well as the scope of this leniency (for example, does it also apply to other instances of שכירות  on shabbos), but that’s some food for thought for now.
These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha.