Nitzavim, Devarim 29:28. Communal Obligation of Mitzvos

Arvus, or more correctly Areivus, means that all Jews have an obligation to see to it that their fellow Jews live Torah lives. Areivus is often translated as meaning the same as Areiv, which is a loan guarantor. In other words, each of us is obligated to fulfill our duty to Hashem, and as guarantors, we also are responsible for our neighbors' duty.

Mishulchan Gavo’ah brings from Reb Baruch Ber (with some changes): we find that if c'v Klal Yisrael is punished for aveiros, because of the din of arvus the tzadikim can be punished. He brings that tzadikim and tashba”r suffer for the resha’im of the generation. Additionally, we find that when pur’anus chas veshalom occurs, it starts from the tzadikim. Reb Baruch Ber asks, the din of arvus as found by a guarantor on a loan is that ein nifra’im min ha’areiv until you make the claim from the actual debtor and he can’t pay the debt. You certainly cannot go to the areiv before going to the primary debtor! He answers that there are two types of arvus. The halacha mentioned is by an areiv stam. But an areiv kablan is a co-signer, not merely a guarantor, and he is equally chayov, he is a primary debtor even though he didn’t borrow the money.  (Technically, there are four kinds of arvus: stam, ahl me'nas she'ipara, kablan, and shlof dotz or nasa ve'nasan be'yad, or according to Rabbeinu Tam toward the end of BB around 174b, five.  However, the distinctions among the last three have no relevance here, since the last group are direct obligations on the areiv, while the first group is primarily on the borrower.  What he means is that there are two categories of arvus.)

He explains that the lomdus of the difference is that an areiv stam accepts responsibility for the result of the debtor’s behavior, that is, if the debtor’s behavior results in default, the areiv must pay. But an areiv kablon accepts the original obligation of the debtor. The latter is also true in the din of arvus of Klal Yisrael. The din of arvus is not just that we are liable for the result of, and therefore punished for, the behavior of others; instead, it is that our chiyuv mitzvos includes seeing to it that others do their mitzvos.

In both monetary Arvus and Mitzva Arvus, you suffer the consequences of the other person's failure to do his duty. But there is a difference: by a monetary debt, if you pay the deadbeat's outstanding loan, you're off the hook. But by mitzvos, it’s not enough for you to do the mitzvah. You can't even do the mitzva twice, once for yourself and once for him. You have to see to it that the other person does it.

I believe that according to this idea of Reb Baruch Ber, the din arvus is not a side-halacha that obligates us to bring Jews to the Torah. It is an additional dimension of every mitzva we are chayav to fulfil. As an areiv kablan, the chiyuv of others to hear the shofar is your chiyuv of Teki'as Shofar. That means that even if you have heard teki'as shofar with the greatest hiddur, if someone has not heard teki'as shofar, and you could have helped him, you were not mekayeim this aspect of the mitzva of tekias shofar.

(By the way, I think this pshat is implicit in what the Rishonim say that you can be motzi a person even on the bracha of a mitzva, even if you have already done the mitzva yourself. They ask, but how can you say "ve'tzivanu to do this mitzva"? You are no longer chayav to do the mitzva! I believe it's a Yerushalmi, but I know it's a Ritva, a Ran and a She'iltos, that the din of Arvus means that if the other person has not been mekayeim the mitzva, then the chiyuv to do this Mitzva still remains upon you. And the nusach habracha is not "vetzivanu to see to it that others do mitzvos", the nusach of the bracha is "vetzivanu to do this mitzva."
The Ritva is in Hilchos Brachos 5:2:

כל הברכות שהם חובה על האדם וחבירו שהוא גדול חייב באותה ברכה כמוהו מוציאו ידי חובתו אע״פ שכבר הוציא עצמו והטעם לפי שכל ישראל ערבין זה לזה וכשחבירו חייב הרי הוא כאילו הוא עצמו חייב ולפיכך יחיד מוציא לחבירו בברכות של ק״ש אע״פ שאין חובה

The Ran is in Rosh HaShanna 29a.

The She'iltos is 54 DH Bram:

ברם צריך אילו מאן דקדיש ונפיק ידי חובתיה מהו לאפוקי לאחרים ידי חובתיהון מי אמרינן כיון דהא איפטר ליה הוה ליה כקטן ואסיר ולא מפיק או דילמא דחיובא הוא מי איכא דבעי קדושי ומיזל לעלם וכל חד וחד מישראל מיחייב בערבותא דחבריה וכמאן דלא איפטר דמי ומפיק אחרים )

Notes:
1. For a similar discussion, see Birkas Shmuel, Kiddushin #27, the chkira he brings from his son in law, R' Reuven Grozovsky, although they're talking about chinuch of limud hatorah and we're talking about mitzvos in general. Others have confused the two sugyos, and assumed that what is true by one is true by the other, but that alleged correlation is purely speculative.
2. See comments, below, from Harav Dr. Eli, Tosfos Sotah 37b, as follows:

See Sotah 37b and Tosfot there D.H. Amar, that counts the number of Britot to be48 x 613 x 603550 (or the last number squared). That is, each one of us took upon itself one obligation to look after Yankel's Shofar and another for Yankel's Mekhashefa Lo Tehaye.

He is referring to the Gemara there

אמר רבי לדברי רבי שמעון בן יהודה איש כפר עכו שאמר משום רבי שמעון אין לך כל מצוה ומצוה שבתורה שלא נכרתו עליה ארבעים ושמנה בריתות של שש מאות אלף ושלשת אלפים וחמש מאות וחמשים נמצא לכל אחד ואחד מישראל שש מאות אלף ושלשת אלפים וחמש מאות וחמשים

and Tosfos there

מר רב משרשיא ערבא וערבא דערבא - כמדומה דהכי בעי למימר דלר"ש בן יהודה קבל עליו כל אחד מישראל לתרי"ג מצות קצ"ח ריבוא ריבואות וח' אלפים ריבואות ותי"ג ריבואות ושבע אלפים ומאתים בריתות לשש מאות אלף ושלשת אלפים וחמשים וחמש מאות בשביל ערבותן אם יעברו עליהן ולרבי אליבא דרבי שמעון ששים ריבוא פעמים ושלשת אלפים ותקנ"ה פעמים חשבון זה בריתות קיבלו עליהן: